Stability of Nonlinear Implicit Differential Equations with Caputo–Katugampola Fractional Derivative

Abstract

The purpose of this paper is to study nonlinear implicit differential equations with the Caputo–Katugampola fractional derivative. By using Gronwall inequality and Banach fixed-point theorem, the existence of the solution of the implicit equation is proved, and the relevant conclusions about the stability of Ulam–Hyers are obtained. Finally, the correctness of the conclusions is verified by an example.

Keywords

• Caputo–Katugampola fractional derivative
• Gronwall inequality
• Banach fixed-point theorem
• Ulam–Hyers stability
• Ulam–Hyers–Rassias stability