Fairouz Tchier | King Saud University (original) (raw)

Papers by Fairouz Tchier

We study a family of random differential equations with boundary conditions. Using a random fixed... more We study a family of random differential equations with boundary conditions. Using a random fixed point theorem, we prove an existence theorem that yields a unique random solution.

We will present some interesting results about the fixed points of some functions with demonic op... more We will present some interesting results about the fixed points of some functions with demonic oper-ators; particularly the function f(X) = Q ∨ P 2X where P< ∧ Q< = Ø, by taking P: = t 2B and Q: = t∼, one gets the demonic semantics we have assigned to while loops in previous papers. We prove that this greatest fixed coincides with the least fixed point with respect to the usual ordering (angelic in-clusion) of the same function. This is followed by an example of application. 1 Relation Algebras Both homogeneous and heterogeneous relation alge-bras are employed in computer science. In this pa-per, we use heterogeneous relation algebras whose definition is taken from [BeZ86, Sch81, ScS93]. (1) Definition. A relation algebra A is a structure (B,∨,∧,−, ◦, ^ ) over a non-empty set B of elements, called relations. The unary operations −, ^ are total whereas the binary operations ∨,∧, ◦ are partial. We denote by B∨R the set of those elements Q ∈ B for which the union R∨Q is defined a...

Revista Mexicana De Fisica, 2017

In this article, the exact-special solutions of the nonlinear dispersion Drinfel’d-Sokolov (short... more In this article, the exact-special solutions of the nonlinear dispersion Drinfel’d-Sokolov (shortly D(m, n)) system are analyzed. We use the ansatz approach and the He’s variational principle for the mentioned equation. The general formulae for the compactons, solitary patterns, solitons and periodic solutions are acquired. These types of solutions are useful and attractive for clarifying some types of nonlinear physical phenomena. These two methods will be used to carry out the integration.

The role of technology and using specialized software in the educational process is growing in re... more The role of technology and using specialized software in the educational process is growing in recent times. Many resources are available both commercial and academic, targeting a wide variety of audiences. In this book we have developed applications that complement the usual topics covered in calculus, such as functions, limits of functions, differentiation, integration, and graphing functions in 2D and 3D. The animations were designed by Maple Soft as an interactive book viewer. It allows the user to read content and play animated illustrations which aids in understanding the mathematical concepts. The animated graphics are simple accessible and can be customized by a user with little programming background. Mathematics is the foundation of many core concepts in science and engineering. A successful career in science and engineering is impossible without a solid mathematical base. However, mathematics are always considered a hard subject because concepts in calculus, and multivari...

Computers, Materials & Continua

Journal of Mathematics, 2021

The term metric or distance of a graph plays a vital role in the study to check the structural pr... more The term metric or distance of a graph plays a vital role in the study to check the structural properties of the networks such as complexity, modularity, centrality, accessibility, connectivity, robustness, clustering, and vulnerability. In particular, various metrics or distance-based dimensions of different kinds of networks are used to resolve the problems in different strata such as in security to find a suitable place for fixing sensors for security purposes. In the field of computer science, metric dimensions are most useful in aspects such as image processing, navigation, pattern recognition, and integer programming problem. Also, metric dimensions play a vital role in the field of chemical engineering, for example, the problem of drug discovery and the formation of different chemical compounds are resolved by means of some suitable metric dimension algorithm. In this paper, we take rotationally symmetric and hexagonal planar networks with all possible faces. We find the sequ...

Entropy

As an extension of intuitionistic fuzzy sets, the theory of picture fuzzy sets not only deals wit... more As an extension of intuitionistic fuzzy sets, the theory of picture fuzzy sets not only deals with the degrees of rejection and acceptance but also considers the degree of refusal during a decision-making process; therefore, by incorporating this competency of picture fuzzy sets, the goal of this study is to propose a novel hybrid model called picture fuzzy soft expert sets by combining picture fuzzy sets with soft expert sets for dealing with uncertainties in different real-world group decision-making problems. The proposed hybrid model is a more generalized form of intuitionistic fuzzy soft expert sets. Some novel desirable properties of the proposed model, namely, subset, equality, complement, union and intersection, are investigated together with their corresponding examples. Two well-known operations AND and OR are also studied for the developed model. Further, a decision-making method supporting by an algorithmic format under the proposed approach is presented. Moreover, an il...

Mathematics

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differen... more Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

Journal of Nonlinear Sciences and Applications

This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensio... more This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensional Burgers equation (BE) by the two variables G G , 1 G expansion method (EM). Obtained soliton solutions are designated in terms of kink, bell-shaped solitary wave, periodic and singular periodic wave solutions. These solutions may be useful and desirable to explain some nonlinear physical phenomena.

Frontiers in Applied Mathematics and Statistics

This paper is devoted to establishing some criteria for the existence of non-trivial solutions fo... more This paper is devoted to establishing some criteria for the existence of non-trivial solutions for a class of fractional q-difference equations involving the p-Laplace operator, which is nowadays known as Lyapunov's inequality. The method employed for it is based on a construction of a Green's function and its maximum value. Parallel to this result, it is worth mentioning that the Hartman-Wintner inequality for the q-fractional p-Laplace boundary value problem is also provided. It covers all previous results known in the literature on the fractional case as well as that on the classical ordinary case. The non-existence of non-trivial solutions to the q-difference fractional p-Laplace equation subject to the Riemann-Liouville mixed boundary conditions will obey such integral inequalities. The tools mainly rely on an integral form of the solution construction of a Green function corresponding to the considered problem and its properties as well as its maximum value in consideration where the kernel is the Green's function. The example that we consider here for applying this result is an eigenvalue fractional problem. To be more specific, we provide an interval where an appropriate Mittag-Leffler function to the given eigenvalue fractional boundary problem has no real zeros.

Journal of Nonlinear Sciences and Applications, Jul 23, 2016

This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensio... more This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensional Burgers equation (BE) by the two variables G G , 1 G expansion method (EM). Obtained soliton solutions are designated in terms of kink, bell-shaped solitary wave, periodic and singular periodic wave solutions. These solutions may be useful and desirable to explain some nonlinear physical phenomena.

Frontiers in Applied Mathematics and Statistics, Apr 22, 2020

This paper is devoted to establishing some criteria for the existence of non-trivial solutions fo... more This paper is devoted to establishing some criteria for the existence of non-trivial solutions for a class of fractional q-difference equations involving the p-Laplace operator, which is nowadays known as Lyapunov's inequality. The method employed for it is based on a construction of a Green's function and its maximum value. Parallel to this result, it is worth mentioning that the Hartman-Wintner inequality for the q-fractional p-Laplace boundary value problem is also provided. It covers all previous results known in the literature on the fractional case as well as that on the classical ordinary case. The non-existence of non-trivial solutions to the q-difference fractional p-Laplace equation subject to the Riemann-Liouville mixed boundary conditions will obey such integral inequalities. The tools mainly rely on an integral form of the solution construction of a Green function corresponding to the considered problem and its properties as well as its maximum value in consideration where the kernel is the Green's function. The example that we consider here for applying this result is an eigenvalue fractional problem. To be more specific, we provide an interval where an appropriate Mittag-Leffler function to the given eigenvalue fractional boundary problem has no real zeros.

Chaos, Solitons & Fractals

Abstract Malkus waterwheel model is a Lorenz type chaotic-physical model expressed in terms of a ... more Abstract Malkus waterwheel model is a Lorenz type chaotic-physical model expressed in terms of a system of nonlinear ordinary differential equations. In this investigation, we consider fractional-order Malkus waterwheel model via Caputo type time derivative and present chaos control, anti-synchronization, numerical solutions of the fractional system. We also associate fractional-order Malkus model with two different optimal control problems. Computational results indicate that this study may serve as a framework for chaotic behavior analysis and approximate solutions of many different parametric systems. The paper may be considered as a novel contribution because optimal control formulations, numerical solutions, stability analysis for fractional-order Malkus model are studied first time in this paper. This research work may be useful for researchers concerning with chaos analysis and approximate solutions of fractional-order chaotic dynamical systems.

Mathematical Methods in the Applied Sciences

Mathematics

An analogous version of Chebyshev inequality, associated with the weighted function, has been est... more An analogous version of Chebyshev inequality, associated with the weighted function, has been established using the pathway fractional integral operators. The result is a generalization of the Chebyshev inequality in fractional integral operators. We deduce the left sided Riemann Liouville version and the Laplace version of the same identity. Our main deduction will provide noted results for an appropriate change to the Pathway fractional integral parameter and the degree of the fractional operator.

Communications in Nonlinear Science and Numerical Simulation

Abstract In this paper, a composite nonlinear feedback technique is proposed for robust tracking ... more Abstract In this paper, a composite nonlinear feedback technique is proposed for robust tracking control of switched systems with unmatched uncertainties and input saturation. The proposed self-tuning integral sliding mode tracker presents a time-varying boundary layer width and a variable control gain, which could improve the transient performance and steady-state accuracy simultaneously. This scheme guarantees robustness against uncertainties, removes reaching phase, and avoids chattering problem. To adapt the variation of the tracking targets, a new scaled nonlinear function is employed. Simulation results are included to exhibit the efficiency of the suggested method.

Entropy

This paper deals with a numerical simulation of fractional conformable attractors of type Rabinov... more This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and β-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and β-conformable attractors are provided to illustrate the effectiveness of the proposed method.

Entropy

In this work, we examine a fractal vehicular traffic flow problem. The partial differential equat... more In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.

Journal of Modern Optics

ABSTRACT This work studies the (2 + 1)-dimensional nonlinear Schrödinger equation which arises in... more ABSTRACT This work studies the (2 + 1)-dimensional nonlinear Schrödinger equation which arises in optical fibre. Grey and black optical solitons of the model are reported using a suitable complex envelope ansatz solution. The integration lead to some certain conditions which must be satisfied for the solitons to exist. On applying the Chupin Liu's theorem to the grey and black optical solitons, we construct new sets of combined optical soliton solutions of the model. Moreover, classification of conservation laws (Cls) of the model is implemented using the multipliers approach. This is achieved by constructing a set of first-order multipliers of a system of nonlinear partial differential equations acquired by transforming the model into real and imaginary components are derived, which are subsequently used to construct the Cls.

The European Physical Journal Plus

Abstract.The current work provides comprehensive investigation for the time fractional third-orde... more Abstract.The current work provides comprehensive investigation for the time fractional third-order variant Boussinesq system (TFTOBS) with Riemann-Liouville (RL) derivative. Firstly, we obtain point symmetries, similarity variables, similarity transformation and reduce the governing equation to a special system of ordinary differential equation (ODE) of fractional order. The reduced equation is in the Erdelyi-Kober (EK) sense. Secondly, we solve the reduced system of ODE using the power series (PS) expansion method. The convergence analysis for the power series solution is analyzed and investigated. Thirdly, the new conservation theorem and the generalization of the Noether operators are applied to construct nonlocal conservation laws (CLs) for the TFTOBS. Finally, we use residual power series (RPS) to extract numerical approximation for the governing equations. Interesting figures that explain the physical understanding for both the explicit and approximate solutions are also presented.

We study a family of random differential equations with boundary conditions. Using a random fixed... more We study a family of random differential equations with boundary conditions. Using a random fixed point theorem, we prove an existence theorem that yields a unique random solution.

We will present some interesting results about the fixed points of some functions with demonic op... more We will present some interesting results about the fixed points of some functions with demonic oper-ators; particularly the function f(X) = Q ∨ P 2X where P< ∧ Q< = Ø, by taking P: = t 2B and Q: = t∼, one gets the demonic semantics we have assigned to while loops in previous papers. We prove that this greatest fixed coincides with the least fixed point with respect to the usual ordering (angelic in-clusion) of the same function. This is followed by an example of application. 1 Relation Algebras Both homogeneous and heterogeneous relation alge-bras are employed in computer science. In this pa-per, we use heterogeneous relation algebras whose definition is taken from [BeZ86, Sch81, ScS93]. (1) Definition. A relation algebra A is a structure (B,∨,∧,−, ◦, ^ ) over a non-empty set B of elements, called relations. The unary operations −, ^ are total whereas the binary operations ∨,∧, ◦ are partial. We denote by B∨R the set of those elements Q ∈ B for which the union R∨Q is defined a...

Revista Mexicana De Fisica, 2017

In this article, the exact-special solutions of the nonlinear dispersion Drinfel’d-Sokolov (short... more In this article, the exact-special solutions of the nonlinear dispersion Drinfel’d-Sokolov (shortly D(m, n)) system are analyzed. We use the ansatz approach and the He’s variational principle for the mentioned equation. The general formulae for the compactons, solitary patterns, solitons and periodic solutions are acquired. These types of solutions are useful and attractive for clarifying some types of nonlinear physical phenomena. These two methods will be used to carry out the integration.

The role of technology and using specialized software in the educational process is growing in re... more The role of technology and using specialized software in the educational process is growing in recent times. Many resources are available both commercial and academic, targeting a wide variety of audiences. In this book we have developed applications that complement the usual topics covered in calculus, such as functions, limits of functions, differentiation, integration, and graphing functions in 2D and 3D. The animations were designed by Maple Soft as an interactive book viewer. It allows the user to read content and play animated illustrations which aids in understanding the mathematical concepts. The animated graphics are simple accessible and can be customized by a user with little programming background. Mathematics is the foundation of many core concepts in science and engineering. A successful career in science and engineering is impossible without a solid mathematical base. However, mathematics are always considered a hard subject because concepts in calculus, and multivari...

Computers, Materials & Continua

Journal of Mathematics, 2021

The term metric or distance of a graph plays a vital role in the study to check the structural pr... more The term metric or distance of a graph plays a vital role in the study to check the structural properties of the networks such as complexity, modularity, centrality, accessibility, connectivity, robustness, clustering, and vulnerability. In particular, various metrics or distance-based dimensions of different kinds of networks are used to resolve the problems in different strata such as in security to find a suitable place for fixing sensors for security purposes. In the field of computer science, metric dimensions are most useful in aspects such as image processing, navigation, pattern recognition, and integer programming problem. Also, metric dimensions play a vital role in the field of chemical engineering, for example, the problem of drug discovery and the formation of different chemical compounds are resolved by means of some suitable metric dimension algorithm. In this paper, we take rotationally symmetric and hexagonal planar networks with all possible faces. We find the sequ...

Entropy

As an extension of intuitionistic fuzzy sets, the theory of picture fuzzy sets not only deals wit... more As an extension of intuitionistic fuzzy sets, the theory of picture fuzzy sets not only deals with the degrees of rejection and acceptance but also considers the degree of refusal during a decision-making process; therefore, by incorporating this competency of picture fuzzy sets, the goal of this study is to propose a novel hybrid model called picture fuzzy soft expert sets by combining picture fuzzy sets with soft expert sets for dealing with uncertainties in different real-world group decision-making problems. The proposed hybrid model is a more generalized form of intuitionistic fuzzy soft expert sets. Some novel desirable properties of the proposed model, namely, subset, equality, complement, union and intersection, are investigated together with their corresponding examples. Two well-known operations AND and OR are also studied for the developed model. Further, a decision-making method supporting by an algorithmic format under the proposed approach is presented. Moreover, an il...

Mathematics

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differen... more Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

Journal of Nonlinear Sciences and Applications

This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensio... more This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensional Burgers equation (BE) by the two variables G G , 1 G expansion method (EM). Obtained soliton solutions are designated in terms of kink, bell-shaped solitary wave, periodic and singular periodic wave solutions. These solutions may be useful and desirable to explain some nonlinear physical phenomena.

Frontiers in Applied Mathematics and Statistics

This paper is devoted to establishing some criteria for the existence of non-trivial solutions fo... more This paper is devoted to establishing some criteria for the existence of non-trivial solutions for a class of fractional q-difference equations involving the p-Laplace operator, which is nowadays known as Lyapunov's inequality. The method employed for it is based on a construction of a Green's function and its maximum value. Parallel to this result, it is worth mentioning that the Hartman-Wintner inequality for the q-fractional p-Laplace boundary value problem is also provided. It covers all previous results known in the literature on the fractional case as well as that on the classical ordinary case. The non-existence of non-trivial solutions to the q-difference fractional p-Laplace equation subject to the Riemann-Liouville mixed boundary conditions will obey such integral inequalities. The tools mainly rely on an integral form of the solution construction of a Green function corresponding to the considered problem and its properties as well as its maximum value in consideration where the kernel is the Green's function. The example that we consider here for applying this result is an eigenvalue fractional problem. To be more specific, we provide an interval where an appropriate Mittag-Leffler function to the given eigenvalue fractional boundary problem has no real zeros.

Journal of Nonlinear Sciences and Applications, Jul 23, 2016

This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensio... more This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensional Burgers equation (BE) by the two variables G G , 1 G expansion method (EM). Obtained soliton solutions are designated in terms of kink, bell-shaped solitary wave, periodic and singular periodic wave solutions. These solutions may be useful and desirable to explain some nonlinear physical phenomena.

Frontiers in Applied Mathematics and Statistics, Apr 22, 2020

This paper is devoted to establishing some criteria for the existence of non-trivial solutions fo... more This paper is devoted to establishing some criteria for the existence of non-trivial solutions for a class of fractional q-difference equations involving the p-Laplace operator, which is nowadays known as Lyapunov's inequality. The method employed for it is based on a construction of a Green's function and its maximum value. Parallel to this result, it is worth mentioning that the Hartman-Wintner inequality for the q-fractional p-Laplace boundary value problem is also provided. It covers all previous results known in the literature on the fractional case as well as that on the classical ordinary case. The non-existence of non-trivial solutions to the q-difference fractional p-Laplace equation subject to the Riemann-Liouville mixed boundary conditions will obey such integral inequalities. The tools mainly rely on an integral form of the solution construction of a Green function corresponding to the considered problem and its properties as well as its maximum value in consideration where the kernel is the Green's function. The example that we consider here for applying this result is an eigenvalue fractional problem. To be more specific, we provide an interval where an appropriate Mittag-Leffler function to the given eigenvalue fractional boundary problem has no real zeros.

Chaos, Solitons & Fractals

Abstract Malkus waterwheel model is a Lorenz type chaotic-physical model expressed in terms of a ... more Abstract Malkus waterwheel model is a Lorenz type chaotic-physical model expressed in terms of a system of nonlinear ordinary differential equations. In this investigation, we consider fractional-order Malkus waterwheel model via Caputo type time derivative and present chaos control, anti-synchronization, numerical solutions of the fractional system. We also associate fractional-order Malkus model with two different optimal control problems. Computational results indicate that this study may serve as a framework for chaotic behavior analysis and approximate solutions of many different parametric systems. The paper may be considered as a novel contribution because optimal control formulations, numerical solutions, stability analysis for fractional-order Malkus model are studied first time in this paper. This research work may be useful for researchers concerning with chaos analysis and approximate solutions of fractional-order chaotic dynamical systems.

Mathematical Methods in the Applied Sciences

Mathematics

An analogous version of Chebyshev inequality, associated with the weighted function, has been est... more An analogous version of Chebyshev inequality, associated with the weighted function, has been established using the pathway fractional integral operators. The result is a generalization of the Chebyshev inequality in fractional integral operators. We deduce the left sided Riemann Liouville version and the Laplace version of the same identity. Our main deduction will provide noted results for an appropriate change to the Pathway fractional integral parameter and the degree of the fractional operator.

Communications in Nonlinear Science and Numerical Simulation

Abstract In this paper, a composite nonlinear feedback technique is proposed for robust tracking ... more Abstract In this paper, a composite nonlinear feedback technique is proposed for robust tracking control of switched systems with unmatched uncertainties and input saturation. The proposed self-tuning integral sliding mode tracker presents a time-varying boundary layer width and a variable control gain, which could improve the transient performance and steady-state accuracy simultaneously. This scheme guarantees robustness against uncertainties, removes reaching phase, and avoids chattering problem. To adapt the variation of the tracking targets, a new scaled nonlinear function is employed. Simulation results are included to exhibit the efficiency of the suggested method.

Entropy

This paper deals with a numerical simulation of fractional conformable attractors of type Rabinov... more This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and β-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and β-conformable attractors are provided to illustrate the effectiveness of the proposed method.

Entropy

In this work, we examine a fractal vehicular traffic flow problem. The partial differential equat... more In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.

Journal of Modern Optics

ABSTRACT This work studies the (2 + 1)-dimensional nonlinear Schrödinger equation which arises in... more ABSTRACT This work studies the (2 + 1)-dimensional nonlinear Schrödinger equation which arises in optical fibre. Grey and black optical solitons of the model are reported using a suitable complex envelope ansatz solution. The integration lead to some certain conditions which must be satisfied for the solitons to exist. On applying the Chupin Liu's theorem to the grey and black optical solitons, we construct new sets of combined optical soliton solutions of the model. Moreover, classification of conservation laws (Cls) of the model is implemented using the multipliers approach. This is achieved by constructing a set of first-order multipliers of a system of nonlinear partial differential equations acquired by transforming the model into real and imaginary components are derived, which are subsequently used to construct the Cls.

The European Physical Journal Plus

Abstract.The current work provides comprehensive investigation for the time fractional third-orde... more Abstract.The current work provides comprehensive investigation for the time fractional third-order variant Boussinesq system (TFTOBS) with Riemann-Liouville (RL) derivative. Firstly, we obtain point symmetries, similarity variables, similarity transformation and reduce the governing equation to a special system of ordinary differential equation (ODE) of fractional order. The reduced equation is in the Erdelyi-Kober (EK) sense. Secondly, we solve the reduced system of ODE using the power series (PS) expansion method. The convergence analysis for the power series solution is analyzed and investigated. Thirdly, the new conservation theorem and the generalization of the Noether operators are applied to construct nonlocal conservation laws (CLs) for the TFTOBS. Finally, we use residual power series (RPS) to extract numerical approximation for the governing equations. Interesting figures that explain the physical understanding for both the explicit and approximate solutions are also presented.