α-Confluent-hyper-geometric stability of ξ-Hilfer impulsive nonlinear fractional Volterra integro-differential equation

Abstract

Abstract The purpose of this work is to investigate the necessary conditions for the existence and uniqueness of solutions, and to introduce a new idea of α-confluent-hyper-geometric stability of an impulsive fractional differential equation with ξ-Hilfer fractional derivative. We use the Diaz–Margolis fixed point theorem to achieve this and illustrate the result with an example.

Keywords

• ξ-Hilfer fractional derivative
• Impulsive fractional differential equation
• α-Confluent-hyper-geometric stability
• Diaz–Margolis fixed point theorem