@article{Aljarallah2026, 
author = {Entesar Aljarallah and K. Venkatachalam and El-sayed El-hady},
title = {Caputo-Fabrizio fractional integro-differential equations: Existence, uniqueness, and    β-Ulam stability results for the solutions in a Banach space},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {1},
pages = {1527-1546},
keywords = {β-Ulam stability, Caputo-Fabrizio fractional integro-differential equation, fractional boundary value problem, non-instantaneous impulsive, integro-differential equations},
url = {https://www.sciopen.com/article/10.3934/math.2026064},
doi = {10.3934/math.2026064},
abstract = {The study of Ulam stability for (functional, differential, difference, integral, integro-differential, and fractional differential) equations heavily relies on inequalities. In such scientific and engineering research, fixed point theorems (FPTs) are essential instruments. This article, on one hand, focused on the    β-Ulam-Hyers stability (   β-UHS) of non-instantaneous impulsive fractional integro-differential equations (N-IIFIDEs) involving the Caputo-Fabrizio fractional derivatives (C-FFDs) in a Banach space. On the other hand, we established the existence and uniqueness (E-UR) of solutions by employing the Banach contraction mapping principle (BCMP) and Krasnoselskii's fixed point theorem (KFPT). To validate the theoretical insights, a carefully crafted example was introduced. In this way, we generalized recent interesting results.}
}