Existence and stability results for impulsive (k,ψ)-Hilfer fractional double integro-differential equation with mixed nonlocal conditions

Abstract

This paper investigates a class of nonlinear impulsive fractional integro-differential equations with mixed nonlocal boundary conditions (multi-point and multi-term) that involves $ (\rho_{k}, \psi_{k}) $-Hilfer fractional derivative. The main objective is to prove the existence and uniqueness of the solution for the considered problem by means of fixed point theory of Banach's and O'Regan's types, respectively. In this contribution, the transformation of the considered problem into an equivalent integral equation is necessary for our main results. Furthermore, the nonlinear functional analysis technique is used to investigate various types of Ulam's stability results. The applications of main results are guaranteed with three numerical examples.

Keywords

• $ (k， \psi) $-hilfer fractional derivative
• impulsive conditions
• nonlocal conditions
• fixed-point theorems
• ulam stability