On the stability of solutions for semilinear fractional differential equation with Caputo derivative

Abstract

In the present paper, several types of stability of the zero solution for a semilinear fractional-order system with exogenous input and Caputo fractional derivative have been studied using the Lyapunov function. In particular, conditional asymptotic stability and conditional Mittag-Leffler stability have been presented by introducing the Mittag-Lefller function of one and two parameters.