Exact solution for commensurate and incommensurate linear systems of fractional differential equations

Abstract

In this paper, we introduce exact solutions for the initial value problems of two classes of a linear system of fractional ordinary differential equations with constant coefficients. This article concerns a linear system of fractional order, where the orders are equal or different rational numbers between zero and one. The conformable fractional derivative presented by [R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, J. Comput. Appl. Math., \(\textbf{264}\) (2014), 65--70] is considered. Two different approaches are adopted to give analytic solutions for fractional order systems. The presented methods are illustrated by analyzing some numerical examples that show the effectiveness of the implemented methods.