Strict Stability of Switched Caputo Fractional Differential Equations

This paper studies a nonlinear system of switched fractional differential equations with generalized Caputo fractional derivatives with respect to another function. The main characteristics of these fractional derivatives are twofold: the lower limit of the fractional derivative equals the switching time, and the applied function in the fractional derivative changes in each interval between two consecutive switching times. Several comparison results and some results for the fractional derivative of convex Lyapunov functions are obtained. Also, strict stability of the zero solution is defined and sufficient conditions for strict stability of the system are obtained. The auxiliary results allow us to avoid the application of fractional derivatives of convex Lyapunov functions in our sufficient conditions. The conditions depend significantly on the type of switching rule and the switching points.