Analysis of a Multiple-Rational-Order Fractional Differential System with Riemann-Liouville Derivative

摘要

The present paper deals with the multiple-rational-order (MRO) fractional differential system equipped with Riemann-Liouville derivative. At .rst, by using the properties of the Riemann-Liouville derivative operator and the fractional integral operator, together with the generalized fractional derivative, we can change the MRO fractional differential system whose the fractional order is any rational into a higher-dimensional system with the same order lying in (0, 1). Second, the stability analysis of linear nonautonomous MRO fractional differential system is given through its equivalent same-order system. Finally, several examples are provided to illustrate the results in this paper.