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Theoretical and numerical studies of fractional Volterra-Fredholm integro-differential equations in Banach space

This paper examines the theoretical, analytical, and approximate solutions of the Caputo fractional Volterra-Fredholm integro-differential equations (FVFIDEs). Utilizing Schaefer’s fixedpoint theorem, the Banach contraction theorem and the Arzelà-Ascoli theorem, we establish some conditions that...

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Main Authors: AlSa'di, Kawthar, Nik Long, N. M. A., Eshkuvatov, Z. K.
Format: Article
Language:English
Published: Universiti Putra Malaysia 2024
Subjects:
Mathematics
Online Access:http://psasir.upm.edu.my/id/eprint/114421/1/114421.pdf
http://psasir.upm.edu.my/id/eprint/114421/
https://mjms.upm.edu.my/lihatmakalah.php?kod=2024/September/18/3/469-489
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spelling my.upm.eprints.1144212025-01-20T01:46:13Z http://psasir.upm.edu.my/id/eprint/114421/ Theoretical and numerical studies of fractional Volterra-Fredholm integro-differential equations in Banach space AlSa'di, Kawthar Nik Long, N. M. A. Eshkuvatov, Z. K. This paper examines the theoretical, analytical, and approximate solutions of the Caputo fractional Volterra-Fredholm integro-differential equations (FVFIDEs). Utilizing Schaefer’s fixedpoint theorem, the Banach contraction theorem and the Arzelà-Ascoli theorem, we establish some conditions that guarantee the existence and uniqueness of the solution. Furthermore, the stability of the solution is proved using the Hyers-Ulam stability and Gronwall-Bellman’s inequality. Additionally, the Laplace Adomian decomposition method (LADM) is employed to obtain the approximate solutions for both linear and non-linear FVFIDEs. The method’s efficiency is demonstrated through some numerical examples. Universiti Putra Malaysia 2024-12-30 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/114421/1/114421.pdf AlSa'di, Kawthar and Nik Long, N. M. A. and Eshkuvatov, Z. K. (2024) Theoretical and numerical studies of fractional Volterra-Fredholm integro-differential equations in Banach space. Malaysian Journal of Mathematical Sciences, 18 (3). pp. 469-489. ISSN 1823-8343 https://mjms.upm.edu.my/lihatmakalah.php?kod=2024/September/18/3/469-489 Mathematics 10.47836/mjms.18.3.01
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
topic Mathematics
spellingShingle Mathematics
AlSa'di, Kawthar
Nik Long, N. M. A.
Eshkuvatov, Z. K.
Theoretical and numerical studies of fractional Volterra-Fredholm integro-differential equations in Banach space
description This paper examines the theoretical, analytical, and approximate solutions of the Caputo fractional Volterra-Fredholm integro-differential equations (FVFIDEs). Utilizing Schaefer’s fixedpoint theorem, the Banach contraction theorem and the Arzelà-Ascoli theorem, we establish some conditions that guarantee the existence and uniqueness of the solution. Furthermore, the stability of the solution is proved using the Hyers-Ulam stability and Gronwall-Bellman’s inequality. Additionally, the Laplace Adomian decomposition method (LADM) is employed to obtain the approximate solutions for both linear and non-linear FVFIDEs. The method’s efficiency is demonstrated through some numerical examples.
format Article
author AlSa'di, Kawthar
Nik Long, N. M. A.
Eshkuvatov, Z. K.
author_facet AlSa'di, Kawthar
Nik Long, N. M. A.
Eshkuvatov, Z. K.
author_sort AlSa'di, Kawthar
title Theoretical and numerical studies of fractional Volterra-Fredholm integro-differential equations in Banach space
title_short Theoretical and numerical studies of fractional Volterra-Fredholm integro-differential equations in Banach space
title_full Theoretical and numerical studies of fractional Volterra-Fredholm integro-differential equations in Banach space
title_fullStr Theoretical and numerical studies of fractional Volterra-Fredholm integro-differential equations in Banach space
title_full_unstemmed Theoretical and numerical studies of fractional Volterra-Fredholm integro-differential equations in Banach space
title_sort theoretical and numerical studies of fractional volterra-fredholm integro-differential equations in banach space
publisher Universiti Putra Malaysia
publishDate 2024
url http://psasir.upm.edu.my/id/eprint/114421/1/114421.pdf
http://psasir.upm.edu.my/id/eprint/114421/
https://mjms.upm.edu.my/lihatmakalah.php?kod=2024/September/18/3/469-489
_version_ 1823093149815275520
score 13.244413

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