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Volume 14
Issue 2
10.3390/axioms14020111
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Analysis of an Abstract Delayed Fractional Integro-Differential System via the α-Resolvent Operator

by
Ishfaq Khan
1,
Akbar Zada
1,*,
Ioan-Lucian Popa
2,3 and
Afef Kallekh
4
1
Department of Mathematics, University of Peshawar, Peshawar 25120, Khyber Pakhtunkhwa, Pakistan
2
Department of Computing, Mathematics and Electronics, “1 Decembrie 1918" University of Alba Iulia, 510009 Alba Iulia, Romania
3
Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
4
Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi Arabia
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(2), 111; https://doi.org/10.3390/axioms14020111
Submission received: 3 December 2024 / Revised: 28 January 2025 / Accepted: 29 January 2025 / Published: 1 February 2025
Versions Notes

Abstract

This paper explores the mild solutions of partial impulsive fractional integro-differential systems of order 1<α<2 in a Banach space. We derive the solution of the system under the assumption that the homogeneous part of the system admits an α-resolvent operator. Krasnoselskii’s fixed point theorem is used for the existence of solution, while uniqueness is ensured using Banach’s fixed point theorem. The stability of the system is analyzed through the framework of Hyers–Ulam stability using Lipschitz conditions. Finally, examples are presented to illustrate the applicability of the theoretical results.
Keywords: integro-differential system; fractional; impulse; delay; stability in terms of Ulam; α-resolvent operator integro-differential system; fractional; impulse; delay; stability in terms of Ulam; α-resolvent operator

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MDPI and ACS Style

Khan, I.; Zada, A.; Popa, I.-L.; Kallekh, A. Analysis of an Abstract Delayed Fractional Integro-Differential System via the α-Resolvent Operator. Axioms 2025, 14, 111. https://doi.org/10.3390/axioms14020111

AMA Style

Khan I, Zada A, Popa I-L, Kallekh A. Analysis of an Abstract Delayed Fractional Integro-Differential System via the α-Resolvent Operator. Axioms. 2025; 14(2):111. https://doi.org/10.3390/axioms14020111

Chicago/Turabian Style

Khan, Ishfaq, Akbar Zada, Ioan-Lucian Popa, and Afef Kallekh. 2025. "Analysis of an Abstract Delayed Fractional Integro-Differential System via the α-Resolvent Operator" Axioms 14, no. 2: 111. https://doi.org/10.3390/axioms14020111

APA Style

Khan, I., Zada, A., Popa, I.-L., & Kallekh, A. (2025). Analysis of an Abstract Delayed Fractional Integro-Differential System via the α-Resolvent Operator. Axioms, 14(2), 111. https://doi.org/10.3390/axioms14020111

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