Ulam stability for nonlinear implicit differential equations with Hilfer-Katugampola fractional derivative and impulses

Abstract

In this paper, we investigate the existence, uniqueness and stability results for a class of nonlinear impulsive Hilfer-Katugampola problems. Our reasoning is founded on the Banach contraction principle and Krasnoselskii's fixed point theorem. In addition, an example is provided to demonstrate the effectiveness of the main results.

Keywords

• hilfer-katugampola fractional derivative
• initial value problem
• existence
• uniqueness
• stability
• fixed point
• impulses