Numerical solutions for systems of fractional differential equations by the decomposition method (original) (raw)

Adomian Decomposition Method for Solving Nonlinear Fractional PDEs

In this paper, we obtain the approximate analytical solution of fractional differential equations with Caputo-Fabrizio fractional derivative by using the fractional Adomian decomposition method. The approximate solutions of nonlinear differential equations with fractional order are successfully obtained using this method , and the result is compared with the result of the existing methods.

Solution of Nonlinear Fractional Differential Equations Using Adomain Decomposition Method

International Journal of Systems Science and Applied Mathematics, 2021

In this paper, Adomian decomposition method (ADM) will apply to solve nonlinear fractional differential equations (FDEs) of Caputo sense. These type of equations is very important in engineering applications such as electrical networks, fluid flow, control theory and fractals theory. ADM give analytical solution in form of series solution so the convergence of the series solution and the error analysis will discuss. In addition, existence and uniqueness of the solution will prove. Some numerical examples will solve to test the validity of the method and the given theorems. A comparison of ADM solution with exact and numerical methods are given.

Some Solutions of Fractional Order Partial Differential Equations Using Adomian Decomposition Method

arXiv: Numerical Analysis, 2017

The Adomian decomposition method is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The aim of this paper is to apply Adomian decomposition method to obtain approximate solutions of nonlinear fractional order partial differential equations with fractional derivatives. The fractional derivatives are taken in the sense of Caputo. The solutions of fractional PDEs are calculated in the form of convergent series. Approximate solutions obtained through the decomposition method have been numerically evaluated, and presented in the form of graphs and tables, and then these solutions are compared with the exact solutions and the results rendering the explicitness, effectiveness and good accuracy of the applied method. Finally, it is observed that the applied method (i.e. Adomian decomposition method) is prevailing and convergent method for the solutions of nonlinear fractional-order partial deferential problems.