New Stability Results for Abstract Fractional Differential Equations with Delay and Non-Instantaneous Impulses

Abstract

This research delves into the field of fractional differential equations with both non-instantaneous impulses and delay within the framework of Banach spaces. Our objective is to establish adequate conditions that ensure the existence, uniqueness, and Ulam–Hyers–Rassias stability results for our problems. The studied problems encompass abstract impulsive fractional differential problems with finite delay, infinite delay, state-dependent finite delay, and state-dependent infinite delay. To provide clarity and depth, we augment our theoretical results with illustrative examples, illustrating the practical implications of our work.

Hyers–Ulam Stability of Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps

“…From [27], it is easy to know that the Mittag-Leffler function E 4α−1,1 (µt 4α−1 ) is a solution of (15). So, the following equality holds:…”

“…Stability is a basic problem of fractional differential equations (FDEs). For recent results on the HUS of FDEs, we refer the reader to some works (see [9][10][11][12][13][14][15]).…”