Iterative procedure for non-linear fractional integro-differential equations via Daftardar–Jafari polynomials

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. Copyright © 2025 The Authors.