EVREN HINCAL - Academia.edu (original) (raw)

Papers by EVREN HINCAL

Numerical Algorithms

In this work, a new optimal iterative algorithm is presented with fourth-order accuracy for root-... more In this work, a new optimal iterative algorithm is presented with fourth-order accuracy for root-finding of real functions. It uses only function as well as derivative evaluation. The algorithm is obtained as a combination of existing third-order methods by specifying a parameter involved. The algorithm is based on local and semilocal analysis and has been specifically designed to improve efficiency and accuracy. The proposed algorithm represents a significant improvement over existing iterative algorithms. In particular, it is tested on a range of polynomial functions and was found to produce accurate and efficient results, with improved performance over existing algorithms in terms of both speed and accuracy. The results demonstrate the effectiveness of the proposed algorithm and suggest that it has great potential for use in a wide range of applications in polynomiography and other areas of mathematical analysis.

Axioms

The term convexity and theory of inequalities is an enormous and intriguing domain of research in... more The term convexity and theory of inequalities is an enormous and intriguing domain of research in the realm of mathematical comprehension. Due to its applications in multiple areas of science, the theory of convexity and inequalities have recently attracted a lot of attention from historians and modern researchers. This article explores the concept of a new group of modified harmonic exponential s-convex functions. Some of its significant algebraic properties are elegantly elaborated to maintain the newly described idea. A new sort of Hermite–Hadamard-type integral inequality using this new concept of the function is investigated. In addition, several new estimates of Hermite–Hadamard inequality are presented to improve the study. These new results illustrate some generalizations of prior findings in the literature.

Fractals

The aim of this study is to design a novel stochastic solver through the Morlet wavelet neural ne... more The aim of this study is to design a novel stochastic solver through the Morlet wavelet neural networks (MWNNs) for solving the mathematical Layla and Majnun (LM) system. The numerical representations of the mathematical LM system have been presented by using the MWNNs along with the optimization is performed through the hybridization of the global and local search schemes. The local active-set (AS) and global genetic algorithm (GA) operators have been used to optimize an error-based merit function using the differential LM model and its initial conditions. The correctness of the MWNNs using the local and global operators is observed through the comparison of the obtained solutions and the Adams scheme, which is used as a reference solution. For the stability of the MWNNs using the global and local operators, the statistical performances with different operators have been provided using the multiple executions to solve the nonlinear LM system.

Fractals

This study shows the design of the Meyer wavelet neural networks (WNNs) to perform the numerical ... more This study shows the design of the Meyer wavelet neural networks (WNNs) to perform the numerical solutions of the spread of computer virus with kill signals, i.e. SEIR-KS system. The optimization of the SEIR-KS system is performed by the Meyer WNNs together with the optimization through the genetic algorithm (GA) and sequential quadratic (SQ) programming, i.e. Meyer WNNs-GASQ programming. A sigmoidal-based log-sigmoid function is implemented as an activation function, while 10 numbers of neurons work with 120 variables throughout this study. The correctness of the proposed Meyer WNNs-GASQP programming is observed through the comparison of the obtained and reference numerical solutions. For the consistency and reliability of the Meyer WNNs-GASQ programming, an analysis based on different statistical procedures is performed using 40 numbers of independent executions. Moreover, the use of different statistical operators like mean, median, minimum, standard deviation and semi-interquart...

Springer Proceedings in Mathematics & Statistics, 2021

Bulletin of the National Research Centre, 2022

Background Hormone production by the thyroid gland is a prime aspect of maintaining body homeosta... more Background Hormone production by the thyroid gland is a prime aspect of maintaining body homeostasis. In this study, the ability of single artificial intelligence (AI)-based models, namely multi-layer perceptron (MLP), support vector machine (SVM), and Hammerstein–Weiner (HW) models, were used in the simulation of thyroidism status. The study's primary aim is to unveil the best performing model for the simulation of thyroidism status using hepatic enzymes and hormones as the independent variables. Three statistical metrics were used in evaluating the performance of the models, namely determination coefficient (R2), correlation coefficient (R), and mean squared error (MSE). Results Considering the quantitative and visual presentation of the results obtained, it has been observed that the MLP model showed higher performance skills than SVM and HW, which improved their performances up to 3.77% and 12.54%, respectively, in the testing stages. Furthermore, to boost the performance of...

Fractal and Fractional, 2022

This research paper deals with the passivity and synchronization problem of fractional-order memr... more This research paper deals with the passivity and synchronization problem of fractional-order memristor-based competitive neural networks (FOMBCNNs) for the first time. Since the FOMBCNNs’ parameters are state-dependent, FOMBCNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, the conventional robust control scheme cannot guarantee the synchronization of FOMBCNNs. Under the framework of the Filippov solution, the drive and response FOMBCNNs are first transformed into systems with interval parameters. Then, the new sufficient criteria are obtained by linear matrix inequalities (LMIs) to ensure the passivity in finite-time criteria for FOMBCNNs with mismatched switching jumps. Further, a feedback control law is designed to ensure the finite-time synchronization of FOMBCNNs. Finally, three numerical cases are given to illustrate the usefulness of our passivity and synchronization results.

13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing — ICAFS-2018, 2018

We developed and studied a mathematical model of HIV+. Two equilibriums points were found, diseas... more We developed and studied a mathematical model of HIV+. Two equilibriums points were found, disease free and endemic equilibrium, and basic reproduction ratio R 0 was also calculated by the use of next generation matrix. Global stability analysis of the equilibria was carried out by the use of Lyapunov function, and it was shown that the stability of the equilibria depends on the magnitude of the basic reproduction ratio. When R 0 \1, the disease free equilibrium is globally asymptotically stable, and disease dies out. On the other hand if R 0 ! 1, the endemic equilibrium is globally asymptotically stable and epidemics occurs. Reported cases of 13646 HIV-1 positive were obtained in the year 2016 from Ministry of Health, Turkey (MOH). This data is used to present the numerical simulations, which supports the analytic result. R 0 was found to be 1.98998, which is bigger than 1, this shows the threat posed by HIV in Turkey.

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2021

In this paper a mathematical model is developed to study the transmission dynamics of HIV infecti... more In this paper a mathematical model is developed to study the transmission dynamics of HIV infection and the effect of horizontal and vertical transmission in Turkey is analyzed. Model is fitted with the use of confirmed HIV cases of both vertical and horizontal transmission from 2011 to 2018. Using the next generation operator the basic reproduction number of the model is obtained, which shows whether the disease persists or dies out in time. Further analysis shows that the model is locally asymptotically stable when the basic reproduction number R0 < 1 and is unstable when R0 > 1. The most sensitive parameters efficient for the control of the infection are obtained using forward normalized sensitivity index. Lastly, the results are obtained with the aid of mesh and contour plots, which show that decreasing the values of transmission rate diseases induced mortality rates and progression rates play a significant role in controlling the spread of HIV transmission.

In this paper, we prove existence of common fixed points for a pair of self mappings in non-norma... more In this paper, we prove existence of common fixed points for a pair of self mappings in non-normal cone pentagonal metric spaces. Our results extend and improve the recent results of Azam et al. [Banach contraction principle on cone rectangular metric spaces, Applicable Analysis and Discrete Mathematics, 3(2), 236–241, 2009], Rashwan and Saleh [Some Fixed Point Theorems in Cone Rectangular Metric Spaces, Mathematica Aeterna, 2(6): 573–587, 2012], Garg and Agarwal, [Banach Contraction Principle on Cone Pentagonal Metric Space, Journal of Advanced Studies in Topology, 3(1), 12–18, 2012], and others. AMS subject classification: 47H10, 54H25.

European Journal of Pure and Applied Mathematics, 2017

In this paper, we prove some common fixed points of three self mappings in non-normal cone pentag... more In this paper, we prove some common fixed points of three self mappings in non-normal cone pentagonal metric spaces. Our results extend and improve the recent results announced by many authors.

Fractal and Fractional, 2021

There is an increasing demand for numerical methods to obtain accurate approximate solutions for ... more There is an increasing demand for numerical methods to obtain accurate approximate solutions for nonlinear models based upon polynomials and transcendental equations under both single and multivariate variables. Keeping in mind the high demand within the scientific literature, we attempt to devise a new nonlinear three-step method with tenth-order convergence while using six functional evaluations (three functions and three first-order derivatives) per iteration. The method has an efficiency index of about 1.4678, which is higher than most optimal methods. Convergence analysis for single and systems of nonlinear equations is also carried out. The same is verified with the approximated computational order of convergence in the absence of an exact solution. To observe the global fractal behavior of the proposed method, different types of complex functions are considered under basins of attraction. When compared with various well-known methods, it is observed that the proposed method a...

Journal of Ocean Engineering and Science, 2021

Abstract The current study employs the novel Hirota bilinear scheme to investigate the nonlinear ... more Abstract The current study employs the novel Hirota bilinear scheme to investigate the nonlinear model. Thus, we acquire some two-wave and breather wave solutions to the governing equation. Breathers are pulsating localized structures that have been used to mimic extreme waves in a variety of nonlinear dispersive media with a narrow banded starting process. Several recent investigations, on the other hand, imply that breathers can survive in more complex habitats, such as random seas, despite the attributed physical restrictions. The authenticity and genuineness of all the acquired solutions agreed with the original equation. In order to shed more light on these novel solutions, we plot the 3-dimensional and contour graphs to the reported solutions with some suitable values. The governing model is also stable because of the idea of linear stability. The study’s findings may help explain the physics behind some of the challenges facing ocean engineers.

AIP Conference Proceedings, 2021

In this study, we developed a mathematical model to study the transmission dynamics of HIV infect... more In this study, we developed a mathematical model to study the transmission dynamics of HIV infection and analyzed the effect of horizontal and vertical transmission in Turkey. We fit the model by using confirmed HIV cases of both vertical and horizontal transmission between 2011 and 2018. By using the next generation operator, we obtained the basic reproduction number of the model which shows whether the disease persists or dies out in time. Further, the most sensitive parameters, that are efficient for the control of the infection, obtained by using forward normalized sensitivity index. The results obtained with the aid of mesh and contour plots.

AIP Conference Proceedings, 2021

Coronavirus disease 2019, also known as Covid-19, is an infectious disease that has infected more... more Coronavirus disease 2019, also known as Covid-19, is an infectious disease that has infected more than nineteen million people all around the world. This virus is a member of coronavirus family but it is the most mortal one. It has named as 2019-nCoV by World Health Organization(WHO) after Chinese Center for Disease Control and Prevention(CDC) discovered a new coronavirus from a swab sample of a patient. As we know this pandemic started December 2019 in China, and it is still spreading and causing deaths all around the world. In this paper, we aimed to estimate the right size of epidemic. For that purpose, we chose 10 countries, which are affected by, and still fighting with this disease, to forecast the upcoming death rates by using the previous week deaths. These 10 countries are Argentina, Austria, Brazil, France, Iran, Italy, Sweden, Turkey, United Kingdom, and United States of America. We used the death data of WHO with assumption that data is accurate. For this estimation, firstly, we used the assumption that the reported death delay distributed according to a gamma distribution. Then, we used a binomial distribution for assumption of deaths. This binomial formula led us to find a posterior distribution which is an extension of Bayes’ theorem for death ratio. Lastly, we compared our estimations with real data.

AIMS Mathematics, 2021

This manuscript is concerned with the stability and synchronization for fractional-order delayed ... more This manuscript is concerned with the stability and synchronization for fractional-order delayed gene regulatory networks (FODGRNs) via Razumikhin approach. First of all, the existence of FODGRNs are established by using homeomorphism theory, 2-norm based on the algebraic method and Cauchy Schwartz inequality. The uniqueness of this work among the existing stability results are, the global Mittag-Leffler stability of FODGRNs is explored based on the fractional-order Lyapunov Razumikhin approach. In the meanwhile, two different controllers such as linear feedback and adaptive feedback control, are designed respectively. With the assistance of fractional Razumikhin theorem and our designed controllers, we have established the global Mittag-Leffler synchronization and adaptive synchronization for addressing master-slave systems. Finally, three numerical cases are given to justify the applicability of our stability and synchronization results.

The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data a... more The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data and a designed mathematical model. The model consisted of two equilibrium points, which were disease-free and epidemic. The stability of the equilibrium points was determined by the magnitude of the basic reproduction number (𝑹𝟎). If 𝑹𝟎 < 1, the disease eventually disappears, if 𝑹𝟎 ≥ 1, the presence of an epidemic is stated. 𝑹𝟎 has been calculated patient zero, with a range of 2.38 to 0.65. Currently, the 𝑹𝟎 for NC was found to be 0.65, indicating that NC is free from the SARS-CoV-2 epidemic.

Chaos, Solitons & Fractals, 2020

It is estimated that, about one billion people mostly from Asia, Sub-Saharan Africa and Latin Ame... more It is estimated that, about one billion people mostly from Asia, Sub-Saharan Africa and Latin America are infected with the Hookworm infection. In this paper, we developed and analyzed a model for the transmission dynamics of Hookworm infection in a human population using Caputo fractional order differential operator. Under Caputo operator, existence and uniqueness for the solutions of the new Hookworm infection model have been analyzed using fixed point theorems. Parameters of the model are estimated with the help of real statistics available for the Hookworm infection from a city of Ghana and the best fit is obtained under the nonlinear least-squares curve fitting technique. Further analysis of the proposed model shows that the disease free (infection-absent) equilibrium is locally asymptotically stable whenever a certain reproduction number R 0 < 1 and the endemic (infection-present) equilibrium point is globally asymptotically stable whenever R 0 < 1 and unstable if R 0 > 1. Using forward normalized sensitivity index, the most sensitive parameters are identified that are essential for control of the infection and we obtained different types of simulations for the proposed Hookworm transmission system with the best fitted fractional order parameter (χ). The modelling results show that the chemotherapy treatment, awareness and improvement of personal hygiene are the best measures to be taken for control of the Hookworm infection among vulnerable community.

Physica A: Statistical Mechanics and its Applications, 2019

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2018

This paper aims to study the transmission dynamics of HIV/AIDS in heterosexual, men having sex wi... more This paper aims to study the transmission dynamics of HIV/AIDS in heterosexual, men having sex with men (MSM)/bisexuals and others in Turkey. Four equilibrium points were obtained which include disease free and endemic equilibrium points. The global stability analysis of the equilibria was carried out using the Lyapunov function which happens to depend on the basic reproduction number R0. If R0 < 1 the disease free equilibrium point is globally asymptotically stable and the disease dies out, and if R0 > 1, the endemic equilibrium point is stable and epidemics will occur. We use raw data obtained from Kocaeli University, PCR Unit, Turkey to analyze and predict the trend of HIV/AIDS among heterosexuals, MSM/bisexual, and others. The basic reproduction number for heterosexuals, MSM/bisexuals, and others was found to be 1.08, 0.6719, and 0.050, respectively. This shows that the threat posed by HIV/AIDS among heterosexuals is greater than followed by MSM/bisexuals, and than the others. So, the relevant authorities should put priorities in containing the disease in order of their threat.

Numerical Algorithms

In this work, a new optimal iterative algorithm is presented with fourth-order accuracy for root-... more In this work, a new optimal iterative algorithm is presented with fourth-order accuracy for root-finding of real functions. It uses only function as well as derivative evaluation. The algorithm is obtained as a combination of existing third-order methods by specifying a parameter involved. The algorithm is based on local and semilocal analysis and has been specifically designed to improve efficiency and accuracy. The proposed algorithm represents a significant improvement over existing iterative algorithms. In particular, it is tested on a range of polynomial functions and was found to produce accurate and efficient results, with improved performance over existing algorithms in terms of both speed and accuracy. The results demonstrate the effectiveness of the proposed algorithm and suggest that it has great potential for use in a wide range of applications in polynomiography and other areas of mathematical analysis.

Axioms

The term convexity and theory of inequalities is an enormous and intriguing domain of research in... more The term convexity and theory of inequalities is an enormous and intriguing domain of research in the realm of mathematical comprehension. Due to its applications in multiple areas of science, the theory of convexity and inequalities have recently attracted a lot of attention from historians and modern researchers. This article explores the concept of a new group of modified harmonic exponential s-convex functions. Some of its significant algebraic properties are elegantly elaborated to maintain the newly described idea. A new sort of Hermite–Hadamard-type integral inequality using this new concept of the function is investigated. In addition, several new estimates of Hermite–Hadamard inequality are presented to improve the study. These new results illustrate some generalizations of prior findings in the literature.

Fractals

The aim of this study is to design a novel stochastic solver through the Morlet wavelet neural ne... more The aim of this study is to design a novel stochastic solver through the Morlet wavelet neural networks (MWNNs) for solving the mathematical Layla and Majnun (LM) system. The numerical representations of the mathematical LM system have been presented by using the MWNNs along with the optimization is performed through the hybridization of the global and local search schemes. The local active-set (AS) and global genetic algorithm (GA) operators have been used to optimize an error-based merit function using the differential LM model and its initial conditions. The correctness of the MWNNs using the local and global operators is observed through the comparison of the obtained solutions and the Adams scheme, which is used as a reference solution. For the stability of the MWNNs using the global and local operators, the statistical performances with different operators have been provided using the multiple executions to solve the nonlinear LM system.

Fractals

This study shows the design of the Meyer wavelet neural networks (WNNs) to perform the numerical ... more This study shows the design of the Meyer wavelet neural networks (WNNs) to perform the numerical solutions of the spread of computer virus with kill signals, i.e. SEIR-KS system. The optimization of the SEIR-KS system is performed by the Meyer WNNs together with the optimization through the genetic algorithm (GA) and sequential quadratic (SQ) programming, i.e. Meyer WNNs-GASQ programming. A sigmoidal-based log-sigmoid function is implemented as an activation function, while 10 numbers of neurons work with 120 variables throughout this study. The correctness of the proposed Meyer WNNs-GASQP programming is observed through the comparison of the obtained and reference numerical solutions. For the consistency and reliability of the Meyer WNNs-GASQ programming, an analysis based on different statistical procedures is performed using 40 numbers of independent executions. Moreover, the use of different statistical operators like mean, median, minimum, standard deviation and semi-interquart...

Springer Proceedings in Mathematics & Statistics, 2021

Bulletin of the National Research Centre, 2022

Background Hormone production by the thyroid gland is a prime aspect of maintaining body homeosta... more Background Hormone production by the thyroid gland is a prime aspect of maintaining body homeostasis. In this study, the ability of single artificial intelligence (AI)-based models, namely multi-layer perceptron (MLP), support vector machine (SVM), and Hammerstein–Weiner (HW) models, were used in the simulation of thyroidism status. The study's primary aim is to unveil the best performing model for the simulation of thyroidism status using hepatic enzymes and hormones as the independent variables. Three statistical metrics were used in evaluating the performance of the models, namely determination coefficient (R2), correlation coefficient (R), and mean squared error (MSE). Results Considering the quantitative and visual presentation of the results obtained, it has been observed that the MLP model showed higher performance skills than SVM and HW, which improved their performances up to 3.77% and 12.54%, respectively, in the testing stages. Furthermore, to boost the performance of...

Fractal and Fractional, 2022

This research paper deals with the passivity and synchronization problem of fractional-order memr... more This research paper deals with the passivity and synchronization problem of fractional-order memristor-based competitive neural networks (FOMBCNNs) for the first time. Since the FOMBCNNs’ parameters are state-dependent, FOMBCNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, the conventional robust control scheme cannot guarantee the synchronization of FOMBCNNs. Under the framework of the Filippov solution, the drive and response FOMBCNNs are first transformed into systems with interval parameters. Then, the new sufficient criteria are obtained by linear matrix inequalities (LMIs) to ensure the passivity in finite-time criteria for FOMBCNNs with mismatched switching jumps. Further, a feedback control law is designed to ensure the finite-time synchronization of FOMBCNNs. Finally, three numerical cases are given to illustrate the usefulness of our passivity and synchronization results.

13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing — ICAFS-2018, 2018

We developed and studied a mathematical model of HIV+. Two equilibriums points were found, diseas... more We developed and studied a mathematical model of HIV+. Two equilibriums points were found, disease free and endemic equilibrium, and basic reproduction ratio R 0 was also calculated by the use of next generation matrix. Global stability analysis of the equilibria was carried out by the use of Lyapunov function, and it was shown that the stability of the equilibria depends on the magnitude of the basic reproduction ratio. When R 0 \1, the disease free equilibrium is globally asymptotically stable, and disease dies out. On the other hand if R 0 ! 1, the endemic equilibrium is globally asymptotically stable and epidemics occurs. Reported cases of 13646 HIV-1 positive were obtained in the year 2016 from Ministry of Health, Turkey (MOH). This data is used to present the numerical simulations, which supports the analytic result. R 0 was found to be 1.98998, which is bigger than 1, this shows the threat posed by HIV in Turkey.

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2021

In this paper a mathematical model is developed to study the transmission dynamics of HIV infecti... more In this paper a mathematical model is developed to study the transmission dynamics of HIV infection and the effect of horizontal and vertical transmission in Turkey is analyzed. Model is fitted with the use of confirmed HIV cases of both vertical and horizontal transmission from 2011 to 2018. Using the next generation operator the basic reproduction number of the model is obtained, which shows whether the disease persists or dies out in time. Further analysis shows that the model is locally asymptotically stable when the basic reproduction number R0 < 1 and is unstable when R0 > 1. The most sensitive parameters efficient for the control of the infection are obtained using forward normalized sensitivity index. Lastly, the results are obtained with the aid of mesh and contour plots, which show that decreasing the values of transmission rate diseases induced mortality rates and progression rates play a significant role in controlling the spread of HIV transmission.

In this paper, we prove existence of common fixed points for a pair of self mappings in non-norma... more In this paper, we prove existence of common fixed points for a pair of self mappings in non-normal cone pentagonal metric spaces. Our results extend and improve the recent results of Azam et al. [Banach contraction principle on cone rectangular metric spaces, Applicable Analysis and Discrete Mathematics, 3(2), 236–241, 2009], Rashwan and Saleh [Some Fixed Point Theorems in Cone Rectangular Metric Spaces, Mathematica Aeterna, 2(6): 573–587, 2012], Garg and Agarwal, [Banach Contraction Principle on Cone Pentagonal Metric Space, Journal of Advanced Studies in Topology, 3(1), 12–18, 2012], and others. AMS subject classification: 47H10, 54H25.

European Journal of Pure and Applied Mathematics, 2017

In this paper, we prove some common fixed points of three self mappings in non-normal cone pentag... more In this paper, we prove some common fixed points of three self mappings in non-normal cone pentagonal metric spaces. Our results extend and improve the recent results announced by many authors.

Fractal and Fractional, 2021

There is an increasing demand for numerical methods to obtain accurate approximate solutions for ... more There is an increasing demand for numerical methods to obtain accurate approximate solutions for nonlinear models based upon polynomials and transcendental equations under both single and multivariate variables. Keeping in mind the high demand within the scientific literature, we attempt to devise a new nonlinear three-step method with tenth-order convergence while using six functional evaluations (three functions and three first-order derivatives) per iteration. The method has an efficiency index of about 1.4678, which is higher than most optimal methods. Convergence analysis for single and systems of nonlinear equations is also carried out. The same is verified with the approximated computational order of convergence in the absence of an exact solution. To observe the global fractal behavior of the proposed method, different types of complex functions are considered under basins of attraction. When compared with various well-known methods, it is observed that the proposed method a...

Journal of Ocean Engineering and Science, 2021

Abstract The current study employs the novel Hirota bilinear scheme to investigate the nonlinear ... more Abstract The current study employs the novel Hirota bilinear scheme to investigate the nonlinear model. Thus, we acquire some two-wave and breather wave solutions to the governing equation. Breathers are pulsating localized structures that have been used to mimic extreme waves in a variety of nonlinear dispersive media with a narrow banded starting process. Several recent investigations, on the other hand, imply that breathers can survive in more complex habitats, such as random seas, despite the attributed physical restrictions. The authenticity and genuineness of all the acquired solutions agreed with the original equation. In order to shed more light on these novel solutions, we plot the 3-dimensional and contour graphs to the reported solutions with some suitable values. The governing model is also stable because of the idea of linear stability. The study’s findings may help explain the physics behind some of the challenges facing ocean engineers.

AIP Conference Proceedings, 2021

In this study, we developed a mathematical model to study the transmission dynamics of HIV infect... more In this study, we developed a mathematical model to study the transmission dynamics of HIV infection and analyzed the effect of horizontal and vertical transmission in Turkey. We fit the model by using confirmed HIV cases of both vertical and horizontal transmission between 2011 and 2018. By using the next generation operator, we obtained the basic reproduction number of the model which shows whether the disease persists or dies out in time. Further, the most sensitive parameters, that are efficient for the control of the infection, obtained by using forward normalized sensitivity index. The results obtained with the aid of mesh and contour plots.

AIP Conference Proceedings, 2021

Coronavirus disease 2019, also known as Covid-19, is an infectious disease that has infected more... more Coronavirus disease 2019, also known as Covid-19, is an infectious disease that has infected more than nineteen million people all around the world. This virus is a member of coronavirus family but it is the most mortal one. It has named as 2019-nCoV by World Health Organization(WHO) after Chinese Center for Disease Control and Prevention(CDC) discovered a new coronavirus from a swab sample of a patient. As we know this pandemic started December 2019 in China, and it is still spreading and causing deaths all around the world. In this paper, we aimed to estimate the right size of epidemic. For that purpose, we chose 10 countries, which are affected by, and still fighting with this disease, to forecast the upcoming death rates by using the previous week deaths. These 10 countries are Argentina, Austria, Brazil, France, Iran, Italy, Sweden, Turkey, United Kingdom, and United States of America. We used the death data of WHO with assumption that data is accurate. For this estimation, firstly, we used the assumption that the reported death delay distributed according to a gamma distribution. Then, we used a binomial distribution for assumption of deaths. This binomial formula led us to find a posterior distribution which is an extension of Bayes’ theorem for death ratio. Lastly, we compared our estimations with real data.

AIMS Mathematics, 2021

This manuscript is concerned with the stability and synchronization for fractional-order delayed ... more This manuscript is concerned with the stability and synchronization for fractional-order delayed gene regulatory networks (FODGRNs) via Razumikhin approach. First of all, the existence of FODGRNs are established by using homeomorphism theory, 2-norm based on the algebraic method and Cauchy Schwartz inequality. The uniqueness of this work among the existing stability results are, the global Mittag-Leffler stability of FODGRNs is explored based on the fractional-order Lyapunov Razumikhin approach. In the meanwhile, two different controllers such as linear feedback and adaptive feedback control, are designed respectively. With the assistance of fractional Razumikhin theorem and our designed controllers, we have established the global Mittag-Leffler synchronization and adaptive synchronization for addressing master-slave systems. Finally, three numerical cases are given to justify the applicability of our stability and synchronization results.

The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data a... more The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data and a designed mathematical model. The model consisted of two equilibrium points, which were disease-free and epidemic. The stability of the equilibrium points was determined by the magnitude of the basic reproduction number (𝑹𝟎). If 𝑹𝟎 < 1, the disease eventually disappears, if 𝑹𝟎 ≥ 1, the presence of an epidemic is stated. 𝑹𝟎 has been calculated patient zero, with a range of 2.38 to 0.65. Currently, the 𝑹𝟎 for NC was found to be 0.65, indicating that NC is free from the SARS-CoV-2 epidemic.

Chaos, Solitons & Fractals, 2020

It is estimated that, about one billion people mostly from Asia, Sub-Saharan Africa and Latin Ame... more It is estimated that, about one billion people mostly from Asia, Sub-Saharan Africa and Latin America are infected with the Hookworm infection. In this paper, we developed and analyzed a model for the transmission dynamics of Hookworm infection in a human population using Caputo fractional order differential operator. Under Caputo operator, existence and uniqueness for the solutions of the new Hookworm infection model have been analyzed using fixed point theorems. Parameters of the model are estimated with the help of real statistics available for the Hookworm infection from a city of Ghana and the best fit is obtained under the nonlinear least-squares curve fitting technique. Further analysis of the proposed model shows that the disease free (infection-absent) equilibrium is locally asymptotically stable whenever a certain reproduction number R 0 < 1 and the endemic (infection-present) equilibrium point is globally asymptotically stable whenever R 0 < 1 and unstable if R 0 > 1. Using forward normalized sensitivity index, the most sensitive parameters are identified that are essential for control of the infection and we obtained different types of simulations for the proposed Hookworm transmission system with the best fitted fractional order parameter (χ). The modelling results show that the chemotherapy treatment, awareness and improvement of personal hygiene are the best measures to be taken for control of the Hookworm infection among vulnerable community.

Physica A: Statistical Mechanics and its Applications, 2019

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2018

This paper aims to study the transmission dynamics of HIV/AIDS in heterosexual, men having sex wi... more This paper aims to study the transmission dynamics of HIV/AIDS in heterosexual, men having sex with men (MSM)/bisexuals and others in Turkey. Four equilibrium points were obtained which include disease free and endemic equilibrium points. The global stability analysis of the equilibria was carried out using the Lyapunov function which happens to depend on the basic reproduction number R0. If R0 < 1 the disease free equilibrium point is globally asymptotically stable and the disease dies out, and if R0 > 1, the endemic equilibrium point is stable and epidemics will occur. We use raw data obtained from Kocaeli University, PCR Unit, Turkey to analyze and predict the trend of HIV/AIDS among heterosexuals, MSM/bisexual, and others. The basic reproduction number for heterosexuals, MSM/bisexuals, and others was found to be 1.08, 0.6719, and 0.050, respectively. This shows that the threat posed by HIV/AIDS among heterosexuals is greater than followed by MSM/bisexuals, and than the others. So, the relevant authorities should put priorities in containing the disease in order of their threat.