Application of ARA-Residual Power Series Method in Solving Systems of Fractional Differential Equations

Abstract

In this research, systems of linear and nonlinear differential equations of fractional order are solved analytically using the novel interesting method: ARA- Residual Power Series (ARA-RPS) technique. This approach technique is based on the combination of the residual power series scheme with the ARA transform to establish analytical approximate solutions in a fast convergent series representation using the concept of the limit. The proposed method needs less time and effort compared with the residual power series technique. To prove the simplicity, applicability, and reliability of the presented method, three numerical examples are proposed and simulated. The obtained results show that the ARA-RPS technique is applicable, simple, and effective to get solutions to linear and nonlinear engineering and physical problems.