Analysis of fractional integro causal evolution impulsive systems on time scales

Abstract

In this article, we study the existence and uniqueness along with Ulam‐type stability of fractional integro causal evolution impulsive systems on time scales. To establish our main results, we use Picard operator along with abstract Grönwall inequality and Gröwall lemma. We constitute some assertions to remove difficulties. At the end, the results are demonstrated via the support of an example.

Existence, uniqueness, and Hyers-Ulam stability of abstract neutral differential equation containing state-dependent fractional integrable impulses

“…Answers to Ulam's question, its attractions and inductions for various situations is an important area of research and is known as Ulam's stability. For detailed information about Ulam's stability, we recommend [12,30,31,34,35,37,[41][42][43][44] and references therein.…”

Ulam Type Stability Results of Nonlinear Impulsive Volterra–Fredholm Integro-Dynamic Adjoint Equations on Time Scale

“…Li and Shen [14] have explored a distinct approach to examine the HU stability of linear differential equations of the second order. Numerous papers have been published representing the HU and HUR stability concepts and the reader is referred to references [15][16][17][18].…”