fateme ghomanjani | Ferdowsi University of Mashhad (original) (raw)

Papers by fateme ghomanjani

Research paper thumbnail of Jordan centralizer maps on trivial extension algebras

Demonstratio Mathematica

The structure of Jordan centralizer maps is investigated on trivial extension algebras. One may o... more The structure of Jordan centralizer maps is investigated on trivial extension algebras. One may obtain some conditions under which a Jordan centralizer map on a trivial extension algebra is a centralizer map. As an application, we characterize the Jordan centralizer map on a triangular algebra.

Research paper thumbnail of On the Lie Centralizers of Quaternion Rings

Kragujevac Journal of Mathematics

In this paper, we investigate the problem of describing the form of Lie centralizers on quaternio... more In this paper, we investigate the problem of describing the form of Lie centralizers on quaternion rings. We provide some conditions under which a Lie centralizer on a quaternion ring is the sum of a centralizer and a center valued map.

Research paper thumbnail of Application of Transcendental Bernstein Polynomials for Solving Two-Dimensional Fractional Optimal Control Problems

Complexity

The aim of this study is to introduce a novel method to solve a class of two-dimensional fraction... more The aim of this study is to introduce a novel method to solve a class of two-dimensional fractional optimal control problems. Since there are some difficulties solving these problems using analytical methods, thus finding numerical methods to approximate their solution is a challenging topic. In this study, we use transcendental Bernstein series. In fact, for solving the problem, we generalize the Bernstein polynomials to a larger class of functions which can provide more accurate approximate solutions. The convergence theorem is proved. Some examples are solved to demonstrate the validity and applicability of this technique. Comparing the results with other methods, we can find the efficiency and applicability of the scheme.

Research paper thumbnail of Modification Of The Hpm By Using Optimal Newton Interpolation Polynomial For Quadratic Riccati Differential Equation

Journal of Mathematics and Computer Science, 2015

In this work, an efficient modification of the homotopy analysis method by using optimal Newton i... more In this work, an efficient modification of the homotopy analysis method by using optimal Newton interpolation polynomials is given for the approximate solutions of the Riccati differential equations. This presented method can be applied to linear and nonlinear models. Examples show that the method is effective.

Research paper thumbnail of A new approach for Volterra functional integral equations with non-vanishing delays and fractional Bagley-Torvik equationss

Proyecciones (Antofagasta), 2021

A numerical technique for Volterra functional integral equations (VFIEs) with non-vanishing delay... more A numerical technique for Volterra functional integral equations (VFIEs) with non-vanishing delays and fractional Bagley-Torvik equation is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are utilized to evaluate the accurate results. The findings for examples figs and tables show that the technique is accurate and simple to use.

Research paper thumbnail of Application of Bezier control points method

Research paper thumbnail of Application of Said Ball Curve for Solving Fractional Differential-Algebraic Equations

Mathematics, 2021

The aim of this paper is to apply the Said Ball curve (SBC) to find the approximate solution of f... more The aim of this paper is to apply the Said Ball curve (SBC) to find the approximate solution of fractional differential-algebraic equations (FDAEs). This method can be applied to solve various types of fractional order differential equations. Convergence theorem of the method is proved. Some examples are presented to show the efficiency and accuracy of the method. Based on the obtained results, the SBC is more accurate than the Bezier curve method.

Research paper thumbnail of Solving a Quadratic Riccati Differential Equation, Multi-Pantograph Delay Differential Equations, and Optimal Control Systems with Pantograph Delays

Axioms, 2020

An effective algorithm for solving quadratic Riccati differential equation (QRDE), multipantograp... more An effective algorithm for solving quadratic Riccati differential equation (QRDE), multipantograph delay differential equations (MPDDEs), and optimal control systems (OCSs) with pantograph delays is presented in this paper. This technique is based on Genocchi polynomials (GPs). The properties of Genocchi polynomials are stated, and operational matrices of derivative are constructed. A collocation method based on this operational matrix is used. The findings show that the technique is accurate and simple to use.

Research paper thumbnail of A new approach for solving linear fractional integro-differential equations and multi variable order fractional differential equations

Proyecciones (Antofagasta), 2020

Research paper thumbnail of Numerical Solution For Nonlinear-quadratic Switching Control Systems With Time Delay

Journal of Mathematics and Computer Science, 2014

Research paper thumbnail of A Meshless Method For Solving Delay Differential Equation Using Radial Basis Functions With Error Analysis

Journal of Mathematics and Computer Science, 2014

In this paper, we present a numerical method for solving delay differential equations (DDEs). The... more In this paper, we present a numerical method for solving delay differential equations (DDEs). The method utilizes radial basis functions (RBFs). Error analysis is presented for this method. Finally, numerical examples are included to show the validity and efficiency of the new technique for solving DDEs.

Research paper thumbnail of A new approach for solving Bratu’s problem

Demonstratio Mathematica, 2019

A numerical technique for one-dimensional Bratu’s problem is displayed in this work. The techniqu... more A numerical technique for one-dimensional Bratu’s problem is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are exhibited to verify the efficiency and accuracy of the proposed technique. In this sequel, the obtained error was shown between the proposed technique, Chebyshev wavelets, and Legendre wavelets. The results display that this technique is accurate.

Research paper thumbnail of Numerical solution for fractional Bratu’s initial value problem

Open Physics, 2017

In this paper, a method for solving fractional Bratu’s initial value problem (FBIVP) is presented... more In this paper, a method for solving fractional Bratu’s initial value problem (FBIVP) is presented. The main idea behind this work is the use of the Bezier curve method (BCM). To show the efficiency of the developed method, numerical results are presented.

Research paper thumbnail of A new approach for numerical solution of a linear system with distributed delays, Volterra delay-integro-differential equations, and nonlinear Volterra-Fredholm integral equation by Bezier curves

Computational and Applied Mathematics, 2015

In this paper, we present Bezier curves method to solve Volterra delay-integro-differential equat... more In this paper, we present Bezier curves method to solve Volterra delay-integro-differential equations. Also, this paper is concerned with a linear system with distributed input delay and input saturation. The approximation process by Bezier curves method is done in two steps. First we divide the time interval into 2k subintervals, second approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree n, and determine Bezier curves on any subinterval by n+1$$n+1 control points. Also, we have used Bezier curves method to solve linear and nonlinear Volterra-Fredholm integral equations, numerically. The proposed method is simple and computationally advantageous. Some numerical examples demonstrate the validity and applicability of the technique.

Research paper thumbnail of Expansion of the Exp-function method for solving systems of two-dimensional Navier–Stokes equations

Journal of Taibah University for Science, 2015

Navier-Stokes equations are the most important equations in fluid dynamics for finding the veloci... more Navier-Stokes equations are the most important equations in fluid dynamics for finding the velocity and pressure functions. The main purpose of this paper is to consider the method for the solution of incompressible Navier-Stokes equations by the Exp-function method.

Research paper thumbnail of Approximate solution for quadratic Riccati differential equation

Journal of Taibah University for Science, 2017

The quadratic Riccati differential equations are a class of nonlinear differential equations of m... more The quadratic Riccati differential equations are a class of nonlinear differential equations of much importance, and play a significant role in many fields of applied science. This paper introduces an efficient method for solving the quadratic Riccati differential equation and the Riccati differential-difference equation. In this technique, the Bezier curves method is considered as an algorithm to find the approximate solution of the nonlinear Riccati equation. Some examples in different cases are given to demonstrate simplicity and efficiency of the proposed method.

Research paper thumbnail of Solving the Optimal Control of Linear Systems via Homotopy Perturbation Method

Intelligent Control and Automation, 2012

In this paper, Homotopy perturbation method is used to find the approximate solution of the optim... more In this paper, Homotopy perturbation method is used to find the approximate solution of the optimal control of linear systems. In this method the initial approximations are freely chosen, and a Homotopy is constructed with an embedding parameter   0,1 p  , which is considered as a "small parameter". Some examples are given in order to find the approximate solution and verify the efficiency of the proposed method.

Research paper thumbnail of Bezier Control Points Method to Solve Scheduling of Injections of Immunotherapeutic Agents

Intelligent Control and Automation, 2012

Cancer immunotherapy aims at enhancing immune system to defend against the tumor. However, it is ... more Cancer immunotherapy aims at enhancing immune system to defend against the tumor. However, it is associated with injecting small doses of tumor-bearing molecules or even using drugs. The problem is that how to schedule these injections effectively and/or how to apply drugs in a way to decrease toxic side effects of drugs such that the tumor growth to be stopped or at least to be limited. Here, the theory of optimal control has been applied to find the optimal schedule of injections of an immunotherapeutic agent against cancer. The numerical method employed works for any dynamic linear system and has almost precise solution. In this work, it was tested for a well known model of the tumor immune system interaction.

Research paper thumbnail of The Bezier Control Points Method for Solving Delay Differential Equation

Intelligent Control and Automation, 2012

In this paper, Bezier surface form is used to find the approximate solution of delay differential... more In this paper, Bezier surface form is used to find the approximate solution of delay differential equations (DDE's). By using a recurrence relation and the traditional least square minimization method, the best control points of residual function can be found where those control points determine the approximate solution of DDE. Some examples are given to show efficiency of the proposed method.

Research paper thumbnail of Optimal Control of Switched Systems based on Bezier Control Points

International Journal of Intelligent Systems and Applications, 2012

This paper presents a new approach for solving optimal control problems for switched systems. We ... more This paper presents a new approach for solving optimal control problems for switched systems. We focus on problems in which a pre-specified sequence of active subsystems is given. For such problems, we need to seek both the optimal switching instants and the optimal continuous inputs. A Bezier control points method is applied for solving an optimal control problem which is supervised by a switched dynamic system. Two steps of approximation exist here. First, the time interval is divided into sub-intervals. Second, the trajectory and control functions are approximatedby Bezier curves in each subinterval. Bezier curves have been considered as piecewise polynomials of degree , then they will be determined by control points on any subinterval. The optimal control problem is there by converted into a nonlinear programming problem (NLP), which can be solved by known algorithms. However in this paper the MATLAB optimization routine FMINCON is used for solving resulting NLP.

Research paper thumbnail of Jordan centralizer maps on trivial extension algebras

Demonstratio Mathematica

The structure of Jordan centralizer maps is investigated on trivial extension algebras. One may o... more The structure of Jordan centralizer maps is investigated on trivial extension algebras. One may obtain some conditions under which a Jordan centralizer map on a trivial extension algebra is a centralizer map. As an application, we characterize the Jordan centralizer map on a triangular algebra.

Research paper thumbnail of On the Lie Centralizers of Quaternion Rings

Kragujevac Journal of Mathematics

In this paper, we investigate the problem of describing the form of Lie centralizers on quaternio... more In this paper, we investigate the problem of describing the form of Lie centralizers on quaternion rings. We provide some conditions under which a Lie centralizer on a quaternion ring is the sum of a centralizer and a center valued map.

Research paper thumbnail of Application of Transcendental Bernstein Polynomials for Solving Two-Dimensional Fractional Optimal Control Problems

Complexity

The aim of this study is to introduce a novel method to solve a class of two-dimensional fraction... more The aim of this study is to introduce a novel method to solve a class of two-dimensional fractional optimal control problems. Since there are some difficulties solving these problems using analytical methods, thus finding numerical methods to approximate their solution is a challenging topic. In this study, we use transcendental Bernstein series. In fact, for solving the problem, we generalize the Bernstein polynomials to a larger class of functions which can provide more accurate approximate solutions. The convergence theorem is proved. Some examples are solved to demonstrate the validity and applicability of this technique. Comparing the results with other methods, we can find the efficiency and applicability of the scheme.

Research paper thumbnail of Modification Of The Hpm By Using Optimal Newton Interpolation Polynomial For Quadratic Riccati Differential Equation

Journal of Mathematics and Computer Science, 2015

In this work, an efficient modification of the homotopy analysis method by using optimal Newton i... more In this work, an efficient modification of the homotopy analysis method by using optimal Newton interpolation polynomials is given for the approximate solutions of the Riccati differential equations. This presented method can be applied to linear and nonlinear models. Examples show that the method is effective.

Research paper thumbnail of A new approach for Volterra functional integral equations with non-vanishing delays and fractional Bagley-Torvik equationss

Proyecciones (Antofagasta), 2021

A numerical technique for Volterra functional integral equations (VFIEs) with non-vanishing delay... more A numerical technique for Volterra functional integral equations (VFIEs) with non-vanishing delays and fractional Bagley-Torvik equation is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are utilized to evaluate the accurate results. The findings for examples figs and tables show that the technique is accurate and simple to use.

Research paper thumbnail of Application of Bezier control points method

Research paper thumbnail of Application of Said Ball Curve for Solving Fractional Differential-Algebraic Equations

Mathematics, 2021

The aim of this paper is to apply the Said Ball curve (SBC) to find the approximate solution of f... more The aim of this paper is to apply the Said Ball curve (SBC) to find the approximate solution of fractional differential-algebraic equations (FDAEs). This method can be applied to solve various types of fractional order differential equations. Convergence theorem of the method is proved. Some examples are presented to show the efficiency and accuracy of the method. Based on the obtained results, the SBC is more accurate than the Bezier curve method.

Research paper thumbnail of Solving a Quadratic Riccati Differential Equation, Multi-Pantograph Delay Differential Equations, and Optimal Control Systems with Pantograph Delays

Axioms, 2020

An effective algorithm for solving quadratic Riccati differential equation (QRDE), multipantograp... more An effective algorithm for solving quadratic Riccati differential equation (QRDE), multipantograph delay differential equations (MPDDEs), and optimal control systems (OCSs) with pantograph delays is presented in this paper. This technique is based on Genocchi polynomials (GPs). The properties of Genocchi polynomials are stated, and operational matrices of derivative are constructed. A collocation method based on this operational matrix is used. The findings show that the technique is accurate and simple to use.

Research paper thumbnail of A new approach for solving linear fractional integro-differential equations and multi variable order fractional differential equations

Proyecciones (Antofagasta), 2020

Research paper thumbnail of Numerical Solution For Nonlinear-quadratic Switching Control Systems With Time Delay

Journal of Mathematics and Computer Science, 2014

Research paper thumbnail of A Meshless Method For Solving Delay Differential Equation Using Radial Basis Functions With Error Analysis

Journal of Mathematics and Computer Science, 2014

In this paper, we present a numerical method for solving delay differential equations (DDEs). The... more In this paper, we present a numerical method for solving delay differential equations (DDEs). The method utilizes radial basis functions (RBFs). Error analysis is presented for this method. Finally, numerical examples are included to show the validity and efficiency of the new technique for solving DDEs.

Research paper thumbnail of A new approach for solving Bratu’s problem

Demonstratio Mathematica, 2019

A numerical technique for one-dimensional Bratu’s problem is displayed in this work. The techniqu... more A numerical technique for one-dimensional Bratu’s problem is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are exhibited to verify the efficiency and accuracy of the proposed technique. In this sequel, the obtained error was shown between the proposed technique, Chebyshev wavelets, and Legendre wavelets. The results display that this technique is accurate.

Research paper thumbnail of Numerical solution for fractional Bratu’s initial value problem

Open Physics, 2017

In this paper, a method for solving fractional Bratu’s initial value problem (FBIVP) is presented... more In this paper, a method for solving fractional Bratu’s initial value problem (FBIVP) is presented. The main idea behind this work is the use of the Bezier curve method (BCM). To show the efficiency of the developed method, numerical results are presented.

Research paper thumbnail of A new approach for numerical solution of a linear system with distributed delays, Volterra delay-integro-differential equations, and nonlinear Volterra-Fredholm integral equation by Bezier curves

Computational and Applied Mathematics, 2015

In this paper, we present Bezier curves method to solve Volterra delay-integro-differential equat... more In this paper, we present Bezier curves method to solve Volterra delay-integro-differential equations. Also, this paper is concerned with a linear system with distributed input delay and input saturation. The approximation process by Bezier curves method is done in two steps. First we divide the time interval into 2k subintervals, second approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree n, and determine Bezier curves on any subinterval by n+1$$n+1 control points. Also, we have used Bezier curves method to solve linear and nonlinear Volterra-Fredholm integral equations, numerically. The proposed method is simple and computationally advantageous. Some numerical examples demonstrate the validity and applicability of the technique.

Research paper thumbnail of Expansion of the Exp-function method for solving systems of two-dimensional Navier–Stokes equations

Journal of Taibah University for Science, 2015

Navier-Stokes equations are the most important equations in fluid dynamics for finding the veloci... more Navier-Stokes equations are the most important equations in fluid dynamics for finding the velocity and pressure functions. The main purpose of this paper is to consider the method for the solution of incompressible Navier-Stokes equations by the Exp-function method.

Research paper thumbnail of Approximate solution for quadratic Riccati differential equation

Journal of Taibah University for Science, 2017

The quadratic Riccati differential equations are a class of nonlinear differential equations of m... more The quadratic Riccati differential equations are a class of nonlinear differential equations of much importance, and play a significant role in many fields of applied science. This paper introduces an efficient method for solving the quadratic Riccati differential equation and the Riccati differential-difference equation. In this technique, the Bezier curves method is considered as an algorithm to find the approximate solution of the nonlinear Riccati equation. Some examples in different cases are given to demonstrate simplicity and efficiency of the proposed method.

Research paper thumbnail of Solving the Optimal Control of Linear Systems via Homotopy Perturbation Method

Intelligent Control and Automation, 2012

In this paper, Homotopy perturbation method is used to find the approximate solution of the optim... more In this paper, Homotopy perturbation method is used to find the approximate solution of the optimal control of linear systems. In this method the initial approximations are freely chosen, and a Homotopy is constructed with an embedding parameter   0,1 p  , which is considered as a "small parameter". Some examples are given in order to find the approximate solution and verify the efficiency of the proposed method.

Research paper thumbnail of Bezier Control Points Method to Solve Scheduling of Injections of Immunotherapeutic Agents

Intelligent Control and Automation, 2012

Cancer immunotherapy aims at enhancing immune system to defend against the tumor. However, it is ... more Cancer immunotherapy aims at enhancing immune system to defend against the tumor. However, it is associated with injecting small doses of tumor-bearing molecules or even using drugs. The problem is that how to schedule these injections effectively and/or how to apply drugs in a way to decrease toxic side effects of drugs such that the tumor growth to be stopped or at least to be limited. Here, the theory of optimal control has been applied to find the optimal schedule of injections of an immunotherapeutic agent against cancer. The numerical method employed works for any dynamic linear system and has almost precise solution. In this work, it was tested for a well known model of the tumor immune system interaction.

Research paper thumbnail of The Bezier Control Points Method for Solving Delay Differential Equation

Intelligent Control and Automation, 2012

In this paper, Bezier surface form is used to find the approximate solution of delay differential... more In this paper, Bezier surface form is used to find the approximate solution of delay differential equations (DDE's). By using a recurrence relation and the traditional least square minimization method, the best control points of residual function can be found where those control points determine the approximate solution of DDE. Some examples are given to show efficiency of the proposed method.

Research paper thumbnail of Optimal Control of Switched Systems based on Bezier Control Points

International Journal of Intelligent Systems and Applications, 2012

This paper presents a new approach for solving optimal control problems for switched systems. We ... more This paper presents a new approach for solving optimal control problems for switched systems. We focus on problems in which a pre-specified sequence of active subsystems is given. For such problems, we need to seek both the optimal switching instants and the optimal continuous inputs. A Bezier control points method is applied for solving an optimal control problem which is supervised by a switched dynamic system. Two steps of approximation exist here. First, the time interval is divided into sub-intervals. Second, the trajectory and control functions are approximatedby Bezier curves in each subinterval. Bezier curves have been considered as piecewise polynomials of degree , then they will be determined by control points on any subinterval. The optimal control problem is there by converted into a nonlinear programming problem (NLP), which can be solved by known algorithms. However in this paper the MATLAB optimization routine FMINCON is used for solving resulting NLP.