Stability analysis of the generalized fractional differential equations with and without exogenous inputs

The stability conditions of the fractional differential equations described by the Caputo generalized fractional derivative have been addressed. The generalized asymptotic stability of a class of the fractional differential equations has been investigated. The fractional input stability in the context of the fractional differential equations described by the Caputo generalized fractional derivative has been introduced. The Lyapunov characterizations of the generalized asymptotic stability and the generalized fractional input stability of the fractional differential equations with or without inputs have been provided. Several examples illustrating the main results of the paper have been proposed. The Caputo generalized fractional derivative and the generalized Gronwall lemma have been used.