Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests Lie group method for fractional partial differential equations. A time-fractional Burgers equation is ...Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained.展开更多
The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this ...The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.展开更多
In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The ob...In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The obtained numerical results were presented in the form of tables and graphics. The difference between the exact solutions and the numerical solutions shows us the effectiveness of the solution using the Mabel program and that this method gave accurate results and was close to the exact solution, in addition to its ability to obtain the numerical solution quickly and efficiently using the Mabel program.展开更多
This manuscript’s aim is to form and examine the numerical simulation of Caputo-time fractional nonlinear Burgers’equation via collocation approach with trigonometric tension B-splines as base functions.First,L 1 di...This manuscript’s aim is to form and examine the numerical simulation of Caputo-time fractional nonlinear Burgers’equation via collocation approach with trigonometric tension B-splines as base functions.First,L 1 discretization formula is utilized for the time fractional derivative and after linearizing the nonlinear term,the trigonometric tension B-spline interpolants are utilized to get a system of simultaneous linear equations that are solved via Gauss elimination method.Thus,numerical approximation at the desired time level is obtained.It is demonstrated via von-Neumann approach that proposed scheme produces stable solutions.The results of six different test examples having their analytical solutions are compared with the results in the literature to validate the accuracy and efficiency of the scheme.展开更多
The generalized fractional Burgers equation is studied in this paper. Using the classical Lie symmetry method, all of the vector fields and symmetry reduction of the equation with nonlinearity are constructed. In part...The generalized fractional Burgers equation is studied in this paper. Using the classical Lie symmetry method, all of the vector fields and symmetry reduction of the equation with nonlinearity are constructed. In particular, an exact solution ＆ provided by using the ansatz method. In addition, other types of exact solution are obtained via the invariant subspace method. Finally, conservation laws for this equation are derived.展开更多
This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differenti...This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differential equation.The proposed scheme has been successfully applied on two very important evolution equations,the space-time fractional differential equation governing wave propagation in low-pass electrical transmission lines equation and the time fractional Burger’s equation.The obtained results show that the proposed method is more powerful,promising and convenient for solving nonlinear fractional differential equations(NFPDEs).To our knowledge,the solutions obtained by the proposed method have not been reported in former literature.展开更多
In this paper we find the solution of linear as well as nonlinear fractional partial differential equations using discrete Adomian decomposition method.Here we develop the discrete Adomian decomposition method to find...In this paper we find the solution of linear as well as nonlinear fractional partial differential equations using discrete Adomian decomposition method.Here we develop the discrete Adomian decomposition method to find the solution of fractional discrete diffusion equation,nonlinear fractional discrete Schrodinger equation,fractional discrete Ablowitz-Ladik equation and nonlinear fractional discrete Burger’s equation.The obtained solution is verified by comparison with exact solution whenα=1.展开更多
文摘Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained.
文摘The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.
文摘In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The obtained numerical results were presented in the form of tables and graphics. The difference between the exact solutions and the numerical solutions shows us the effectiveness of the solution using the Mabel program and that this method gave accurate results and was close to the exact solution, in addition to its ability to obtain the numerical solution quickly and efficiently using the Mabel program.
文摘This manuscript’s aim is to form and examine the numerical simulation of Caputo-time fractional nonlinear Burgers’equation via collocation approach with trigonometric tension B-splines as base functions.First,L 1 discretization formula is utilized for the time fractional derivative and after linearizing the nonlinear term,the trigonometric tension B-spline interpolants are utilized to get a system of simultaneous linear equations that are solved via Gauss elimination method.Thus,numerical approximation at the desired time level is obtained.It is demonstrated via von-Neumann approach that proposed scheme produces stable solutions.The results of six different test examples having their analytical solutions are compared with the results in the literature to validate the accuracy and efficiency of the scheme.
文摘The generalized fractional Burgers equation is studied in this paper. Using the classical Lie symmetry method, all of the vector fields and symmetry reduction of the equation with nonlinearity are constructed. In particular, an exact solution ＆ provided by using the ansatz method. In addition, other types of exact solution are obtained via the invariant subspace method. Finally, conservation laws for this equation are derived.
文摘This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differential equation.The proposed scheme has been successfully applied on two very important evolution equations,the space-time fractional differential equation governing wave propagation in low-pass electrical transmission lines equation and the time fractional Burger’s equation.The obtained results show that the proposed method is more powerful,promising and convenient for solving nonlinear fractional differential equations(NFPDEs).To our knowledge,the solutions obtained by the proposed method have not been reported in former literature.
基金to UGC New Delhi,India for financial support under the scheme”Research Fellowship in Science for Meritorious Students”vide letter No.F.4-3/2006(BSR)/11-78/2008(BSR).
文摘In this paper we find the solution of linear as well as nonlinear fractional partial differential equations using discrete Adomian decomposition method.Here we develop the discrete Adomian decomposition method to find the solution of fractional discrete diffusion equation,nonlinear fractional discrete Schrodinger equation,fractional discrete Ablowitz-Ladik equation and nonlinear fractional discrete Burger’s equation.The obtained solution is verified by comparison with exact solution whenα=1.
