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

2025/02/17 by Qasim Khan, Khan, Qasim, Anthony Suen +1
Mathematics · #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2502.11676

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.

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