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

Benchaib, Abdellatif; Salim, Abdelkrim; Abbas, Saïd; Benchohra, Mouffak

doi:10.3390/math11163490

Open AccessArticle

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

¹

Laboratory of Dynamical Systems and Applications, University of Tlemcen, Tlemcen 13000, Algeria

²

Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria

³

Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria

⁴

Department of Electronics, University of Saïda–Dr. Moulay Tahar, P.O. Box 138, Saïda 20000, Algeria

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2023, 11(16), 3490; https://doi.org/10.3390/math11163490

Submission received: 18 July 2023 / Revised: 8 August 2023 / Accepted: 10 August 2023 / Published: 12 August 2023

(This article belongs to the Special Issue Recent Research on Fractional Calculus: Theory and Applications)

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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

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MDPI and ACS Style

Benchaib, A.; Salim, A.; Abbas, S.; Benchohra, M. New Stability Results for Abstract Fractional Differential Equations with Delay and Non-Instantaneous Impulses. Mathematics 2023, 11, 3490. https://doi.org/10.3390/math11163490

AMA Style

Benchaib A, Salim A, Abbas S, Benchohra M. New Stability Results for Abstract Fractional Differential Equations with Delay and Non-Instantaneous Impulses. Mathematics. 2023; 11(16):3490. https://doi.org/10.3390/math11163490

Chicago/Turabian Style

Benchaib, Abdellatif, Abdelkrim Salim, Saïd Abbas, and Mouffak Benchohra. 2023. "New Stability Results for Abstract Fractional Differential Equations with Delay and Non-Instantaneous Impulses" Mathematics 11, no. 16: 3490. https://doi.org/10.3390/math11163490

APA Style

Benchaib, A., Salim, A., Abbas, S., & Benchohra, M. (2023). New Stability Results for Abstract Fractional Differential Equations with Delay and Non-Instantaneous Impulses. Mathematics, 11(16), 3490. https://doi.org/10.3390/math11163490

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

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