Stability analysis for boundary value problems with generalized nonlocal condition via Hilfer–Katugampola fractional derivative

Abstract

Abstract In this research, we present the stability analysis of a fractional differential equation of a generalized Liouville–Caputo-type (Katugampola) via the Hilfer fractional derivative with a nonlocal integral boundary condition. Besides, we derive the relation between the proposed problem and the Volterra integral equation. Using the concepts of Banach and Krasnoselskii’s fixed point theorems, we investigate the existence and uniqueness of solutions to the proposed problem. Finally, we present two examples to clarify the abstract result.

Keywords

• Hilfer fractional derivative
• Stability
• Volterra integral equation
• Nonlocal integral condition