On Multi-Order Fractional Differential Equation: An Analytical Solution Subject to Existing NumericalSolution

Abstract

The constraints and limits of perturbation methods can be overcome by HAM, and hence allowing us to investigate severely nonlinear issues that would otherwise be impossible to investigate. In light of these considerations, the system of fractional differential equations generated by a multi-order fractional differential equation is solved with the homotopy analysis method. Such equation was initially numerically solved by Kai and Ford [5]. In this context, the Caputo sense is used to define the fractional derivative. Our current findings on the use of HAM to solve a system of fractional differential equations might prove useful to anyone seeking an analytical solution to such problems from an engineering point of view.