Terminal Value Problem for Differential Equations with Hilfer–Katugampola Fractional Derivative

Abstract

We present in this work the existence results and uniqueness of solutions for a class of boundary value problems of terminal type for fractional differential equations with the Hilfer–Katugampola fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Banach contraction principle and Krasnoselskii’s fixed point theorem. We illustrate our main findings, with a particular case example included to show the applicability of our outcomes.

Keywords

• Hilfer–Katugampola fractional derivative
• terminal value problem
• existence
• uniqueness
• fixed point