A robust computational analysis of residual power series involving general transform to solve fractional differential equations

In this paper, we provide a new semi-analytical approach, General Residual Power Series Method (GRPSM), to solve fractional differential equations (FDEs). This technique is simple and effective for finding an accurate and approximate solution to linear and nonlinear FDEs. Furthermore, the graphical and numerical results are described in various fractional orders. The solution obtained by GRPSM is compared with Adomian decomposition and Homotopy analysis transform method. We have solved fractional ordered gas dynamics equations and drainage equations using GRPSM, to show the applicability and simplicity of this method. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

In this paper, a new semi-analytical approach called General Residual Power Series Method (GRPSM) is proposed for solving fractional differential equations (FDEs). This method is simple and effective in obtaining accurate and approximate solutions for both linear and nonlinear FDEs. The graphical and numerical results are presented for various fractional orders. A comparison with other methods, such as Adomian decomposition and Homotopy analysis transform method, shows the applicability and simplicity of GRPSM. Moreover, the method is successfully applied to solve fractional ordered gas dynamics equations and drainage equations, demonstrating its practicality.