Improved analytical approach for the solution of non-integer order differential equations

Abstract

This work proposes a method of solving system of both integer and fractional order differential equations. The method is developed through an elegant combination of an integral transform: Shehu transform and homotopy analysis method (STHAM). Caputo definition is adopted while interpreting the non-integer derivative, while homotopy derivatives are employed to overcome the non-linearities encountered. Implementation of the proposed method on selected problems from the literature reveals its reliability, as the result obtained through it compared favorably with those in the literature. The results are equally presented in 3D graphs.