On the Stability Properties of Retarded Volterra Integro-Fractional Differential Equations With Caputo Derivative

Abstract

In this paper, the direct Lyapunov method is extended to fractional case of Volterra integro-Caputo fractional differential equations with delays. Two types of homogeneous scalar Voterra integro-Caputo fractional differential equations with delays are studied. Three types of fractional derivatives of Lyapunov functions known in the literature are given. Uniform stability of trivial solution of that retarded IFrDEs is investigated using the Razumikhin method and different types of fractional derivatives of Lyapunov functions. Examples to show the application of the theorems are provided.