On the Perturbation-Iteration Algorithm for System of Fractional Differential Equations

TL;DR

This paper introduces the perturbation-iteration algorithm (PIA) as a new approach for solving systems of fractional differential equations, demonstrating its effectiveness through numerical comparisons.

Contribution

First application of PIA to systems of fractional differential equations, showing it is a simple, reliable, and powerful solution method.

Findings

PIA provides accurate numerical solutions

PIA outperforms existing methods in efficiency

The method is applicable to nonlinear FDEs

Abstract

In this study, perturbation-iteration algorithm, namely PIA, is applied to solve some types of system of fractional differential equations (FDEs) for the first time. To illustrate the efficiency of the method, numerical solutions are compared with the results published in the literature by considering some FDEs. The results confirm that the PIA is powerful, simple and reliable method for solving system of nonlinear fractional differential equations.