Approximate Solution of the Conformable Integro-Differential Equations

Abstract

In this paper, fractional linear and nonlinear integro-differential equations are solved by using an iteration method. Fractional derivative and fractional integral are considered in the conformable sense. The conformable integro-differential equation is converted to a conformable integral equation. Then, the conformable integral equation leads to an iteration sequence, the limit of which is a solution of the conformable integro-differential equation. In addition, stability and convergence analysis of the presented method are investigated. The applicability of the presented method is also shown by using numerical examples. © 2025 The Author(s). Published by Miskolc University Press. This is an open access article under the license CC BY 4.0.