ON THE STABILITY OF DIFFERENTIAL SYSTEMS INVOLVING ψ-HILFER FRACTIONAL DERIVATIVE

Abstract

This paper deals with the stability of solutions to ψ-Hilfer fractional differential systems. We derive the fundamental solution for the system by using the generalized Laplacetransform and the Mittag-Leffler function with two parameters. In addition, we obtained some necessary conditions on the stability of the solutions to linear fractional differential systems for homogeneous, non-homogeneous and non-autonomous cases. Numerical examplesare also given to illustrate the behavior of solutions.