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

Abdellatif Benchaib, Abdelkrim Salim (), Saïd Abbas and Mouffak Benchohra
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Abdellatif Benchaib: Laboratory of Dynamical Systems and Applications, University of Tlemcen, Tlemcen 13000, Algeria
Abdelkrim Salim: Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria
Saïd Abbas: Department of Electronics, University of Saïda–Dr. Moulay Tahar, P.O. Box 138, Saïda 20000, Algeria
Mouffak Benchohra: Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria

Mathematics, 2023, vol. 11, issue 16, 1-19

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.

Keywords: Caputo fractional-order derivative; mild solution; impulse; delay; Ulam stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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