Analysis of an Abstract Delayed Fractional Integro-Differential System via the <i>α</i>-Resolvent Operator
This paper explores the mild solutions of partial impulsive fractional integro-differential systems of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo>&...
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2025-02-01
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| author | Ishfaq Khan Akbar Zada Ioan-Lucian Popa Afef Kallekh |
| author_facet | Ishfaq Khan Akbar Zada Ioan-Lucian Popa Afef Kallekh |
| author_sort | Ishfaq Khan |
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| description | This paper explores the mild solutions of partial impulsive fractional integro-differential systems of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>α</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula> in a Banach space. We derive the solution of the system under the assumption that the homogeneous part of the system admits an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-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. |
| format | Article |
| id | doaj-art-3d683a4e17874b6eb46b8a30f6de5f0e |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-3d683a4e17874b6eb46b8a30f6de5f0e2025-08-20T02:44:34ZengMDPI AGAxioms2075-16802025-02-0114211110.3390/axioms14020111Analysis of an Abstract Delayed Fractional Integro-Differential System via the <i>α</i>-Resolvent OperatorIshfaq Khan0Akbar Zada1Ioan-Lucian Popa2Afef Kallekh3Department of Mathematics, University of Peshawar, Peshawar 25120, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25120, Khyber Pakhtunkhwa, PakistanDepartment of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, RomaniaDepartment of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi ArabiaThis paper explores the mild solutions of partial impulsive fractional integro-differential systems of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>α</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula> in a Banach space. We derive the solution of the system under the assumption that the homogeneous part of the system admits an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-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.https://www.mdpi.com/2075-1680/14/2/111integro-differential systemfractionalimpulsedelaystability in terms of Ulam<i>α</i>-resolvent operator |
| spellingShingle | Ishfaq Khan Akbar Zada Ioan-Lucian Popa Afef Kallekh Analysis of an Abstract Delayed Fractional Integro-Differential System via the <i>α</i>-Resolvent Operator Axioms integro-differential system fractional impulse delay stability in terms of Ulam <i>α</i>-resolvent operator |
| title | Analysis of an Abstract Delayed Fractional Integro-Differential System via the <i>α</i>-Resolvent Operator |
| title_full | Analysis of an Abstract Delayed Fractional Integro-Differential System via the <i>α</i>-Resolvent Operator |
| title_fullStr | Analysis of an Abstract Delayed Fractional Integro-Differential System via the <i>α</i>-Resolvent Operator |
| title_full_unstemmed | Analysis of an Abstract Delayed Fractional Integro-Differential System via the <i>α</i>-Resolvent Operator |
| title_short | Analysis of an Abstract Delayed Fractional Integro-Differential System via the <i>α</i>-Resolvent Operator |
| title_sort | analysis of an abstract delayed fractional integro differential system via the i α i resolvent operator |
| topic | integro-differential system fractional impulse delay stability in terms of Ulam <i>α</i>-resolvent operator |
| url | https://www.mdpi.com/2075-1680/14/2/111 |
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