Homotopy Perturbation Technique for Fractional Volterra and Fredholm Integro Differential Equations

Abstract

This work focuses on fractional calculus, which is calculus with fractional derivatives. The ideal is that we have the first derivative, which is velocity, and the second derivative, which is acceleration, and that we can have any derivative between the first and second derivatives. To this end, the Homotopy Perturbation Technique (HPT) is used to approximate the solution of Fractional Integro-Differential Equations (FIDEs) with the Caputo derivative, which provides less rigorous works with improved accuracy. To demonstrate the method, some numerical examples are provided. The findings achieved by the current method are found to be comparable to the exact result.