Existence analysis on multi-derivative nonlinear fractional neutral impulsive integro-differential equations

Abstract

This article utilizes the Atangana–Baleanu (AB) fractional derivative to examine the behavior of multi-derivative fractional neutral impulsive integro-differential equations under non-local conditions. To demonstrate the existence, uniqueness, and controllability of the solutions, we utilize fixed point theory as our primary analytical tool. Furthermore, we include a detailed example to illustrate and validate the theoretical results obtained from our study.

Keywords

• Fractional calculus
• Gronwall–Bellman inequality
• Fixed point theory
• Controllability
• Atangana–Baleanu derivative