A novel approach for solving partial integro-differential equations using optimal perturbation iteration method

Noor S.  Rahmah; Osama H.  Mohammed

doi:10.6180/jase.202510_28(10).0002

A novel approach for solving partial integro-differential equations using optimal perturbation iteration method

Noor S. Rahmah¹This email address is being protected from spambots. You need JavaScript enabled to view it. and Osama H. Mohammed²

¹Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Jadriya, Baghdad, Iraq

²Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Jadriya, Baghdad, Iraq

Received: September 29, 2024
Accepted: November 25, 2024
Publication Date: January 13, 2025

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202510_28(10).0002

We present a novel and effective algorithm to solve non-linear fractional order partial integro-differential equations whichisbasedontheoptimalperturbationiteration transform method. Thefractionalorderderivative will be in the Caputo-Atangana-Baleanu sense. The optimal perturbation iteration transform method is a combination between the Laplace transform and the perturbation iteration algorithm. The solution is described by the suggested method as a quickly convergent series. To demonstrates the applicability of the proposed technique, two model examples are solved. The present paper also unveils that optimal perturbation iteration transform method quickly converges to the precise answers of the provided equations at a reduced iteration value.

Keywords: Perturbation iteration method, Partial integro-differential equations, Fractional calculus, Least squares method.

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