Analytic study on linear systems of fractional differential equations

Abstract

An analytic study on linear systems of fractional differential equations with constant coefficients is presented. We briefly describe the issues of existence, uniqueness and stability of the solutions for two classes of linear fractional differential systems. This paper deals with systems of differential equations of fractional order, where the orders are equal to real number or rational numbers between zero and one. Exact solutions for initial value problems of linear fractional differential systems are analytically derived. Existence and uniqueness results are proved for two classes. The presented results are illustrated by analyzing some examples to demonstrate the effectiveness of the presented analytical approaches.