Hyers-Ulam stability of fractional integro-differential equation with a positive constant coefficient involving the generalized Caputo fractional derivative

Abstract

The purpose of this paper is to investigate the existence and uniqueness of a solution and the continuous dependence on the input data of the solution of integro-differential equations with a positive constant coefficient involving  fractional order derivative (FIDEs). In addition, we also provide the sufficient conditions for the Hyers-Ulam stability (HU-stability) and the Hyers-Ulam-Rassias  stability (HUR-stability) of FIDEs. Finally, the HUR-stability of the well-known model of RLC circuit in the form of FIDEs is also surveyed.