Iterative Procedure for Non-Linear Fractional Integro-Differential Equations via Daftardar--Jafari Polynomials

TL;DR

This paper presents the Iterative Aboodh Transform Method (IATM) using Daftardar--Jafari polynomials to efficiently solve non-linear fractional integro-differential equations with higher accuracy and simplicity compared to existing methods.

Contribution

It introduces a new iterative approach employing Daftardar--Jafari polynomials for solving non-linear FPIDEs, offering simplicity and improved accuracy over traditional polynomial methods.

Findings

The proposed method achieves higher accuracy in solutions.

Daftardar--Jafari polynomials are simpler to compute than Adomian polynomials.

Numerical results demonstrate the effectiveness of the IATM.

Abstract

In this paper, we introduce a novel approach called the Iterative Aboodh Transform Method (IATM) which utilizes Daftardar--Jafari polynomials for solving non-linear problems. Such method is employed to derive solutions for non-linear fractional partial integro-differential equations (FPIDEs). The key novelty of the suggested method is that it can be used for handling solutions of non-linear FPIDEs in a very simple and effective way. {More precisely, we show that Daftardar--Jafari polynomials have simple calculations as compared to Adomian polynomials with higher accuracy}. The results obtained within the Daftardar--Jafari polynomials are demonstrated with graphs and tables, and the IATM's absolute error confirms the higher accuracy of the suggested method.