Stability of the mixed Caputo fractional integro-differential equation by means of weighted space method

Abstract

In this research work, we consider a class of nonlinear fractional integro-differential equations containing Caputo fractional derivative and integral derivative. We discuss the stabilities of Ulam-Hyers, Ulam-Hyers-Rassias, semi-Ulam-Hyers-Rassias for the nonlinear fractional integro-differential equations in terms of weighted space method and Banach fixed-point theorem. After the demonstration of our results, an example is given to illustrate the results we obtained.

Keywords

• mixed caputo fractional derivative
• weighted space method
• ulam-hyers stability
• ulam-hyers-rassias stability
• semi-ulam-hyers-rassias stability