ARA-residual power series method for solving partial fractional differential equations

Abstract

In this article a new approach in solving time fractional partial differential equations (TFPDEs) is introduced, that is, the ARA-residual power series method. The main idea of this technique, depends on applying the ARA-transform and using Taylor's expansion to construct approximate series solutions. The procedure of getting the approximate solutions for nonlinear TFPDEs is a difficult mission, the ARA-residual power series method over comes this trouble throughout expressing the solution in a series form then obtain the series coefficients using the idea of the residual function and the concept of the limit at infinity. This method is efficient and applicable to solve a wide family of TFPDEs. Four attractive applications are considered to show the speed and the strength of the proposed method in constructing solitary series solutions of the target equations.

Keywords

• Fractional initial value problems
• Caputo’s derivative operator
• ARA-residual power series
• Fractional power series
• ARA transform
• Time-fractional partial differential equations