Caputo-Fabrizio fractional integro-differential equations: Existence, uniqueness, and $ \beta $-Ulam stability results for the solutions in a Banach space

Entesar Aljarallah; K. Venkatachalam; El-sayed El-hady; Entesar Aljarallah; K. Venkatachalam; El-sayed El-hady

doi:10.3934/math.2026064

AIMS Mathematics

2026, Volume 11, Issue 1: 1527-1546. doi: 10.3934/math.2026064

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Caputo-Fabrizio fractional integro-differential equations: Existence, uniqueness, and $ \beta $-Ulam stability results for the solutions in a Banach space

1.
Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia
2.
Department of Mathematics, Nandha Engineering College, Erode-52, Tamil Nadu, India

Received: 30 November 2025 Revised: 11 January 2026 Accepted: 14 January 2026 Published: 19 January 2026
MSC : 34A08, 47G20

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 $ \beta $-Ulam-Hyers stability ($ \beta $-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.
Citation: Entesar Aljarallah, K. Venkatachalam, El-sayed El-hady. Caputo-Fabrizio fractional integro-differential equations: Existence, uniqueness, and $ \beta $-Ulam stability results for the solutions in a Banach space[J]. AIMS Mathematics, 2026, 11(1): 1527-1546. doi: 10.3934/math.2026064

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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 $ \beta $-Ulam-Hyers stability ($ \beta $-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.

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