Investigating a generalized Hilfer-type fractional differential equation with two-point and integral boundary conditions

Abstract

In this paper, we investigate a nonlinear generalized fractional differential equation with two-point and integral boundary conditions in the frame of κ-Hilfer fractional derivative. The existence and uniqueness results are obtained using Krasnoselskii and Banach's fixed point theorems. We analyze different types of stability results of the proposed problem by using some mathematical methodologies. At the end of the paper, we present a numerical example to demonstrate and validate our findings.

Keywords

• κ-hilfer fractional derivative
• boundary conditions
• fixed point theorem