Homotopy methods for fractional linear/nonlinear differential equations with a local derivative operator

Abstract

In this paper, we consider some linear/nonlinear differential equations (DEs) containing conformable derivative operator. We obtain approximate solutions of these mentioned DEs in the form of infinite series which converges rapidly to their exact values by using and homotopy analysis method (HAM) and modified homotopy perturbation method (MHPM). Using the conformable operator in solutions of different types of DEs makes the solution steps are computable easily. Especially, the conformable operator has been used in modelling DEs and identifying particular problems such as biological, engineering, economic sciences and other some important fields of application. In this context, the aim of this study is to solve some illustrative linear/nonlinear problems as mathematically and to compare the exact solutions with the obtained solutions by considering some plots. Moreover, it is an aim to show the authenticity, applicability, and suitability of the methods constructed with the conformable operator.