Lyapunov stability solutions of fractional integrodifferential equations

Abstract

Lyapunov stability and asymptotic stability conditions for the solutions of the fractional integrodiffrential equations x(α)(t)=f(t,x(t))+∫t0tk(t,s,x(s))ds, 0<α≤1, with the initial condition x(α−1)(t0)=x0, have been investigated. Our methods are applications of Gronwall's lemma and Schwartz inequality.