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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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/114421/ http://psasir.upm.edu.my/id/eprint/114421/1/114421.pdf |
| _version_ | 1848866489181929472 |
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| 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 |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T14:21:25Z |
| format | Article |
| id | upm-114421 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:21:25Z |
| publishDate | 2024 |
| publisher | Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-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 |
| 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 |
| title | 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_short | 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 |
| topic | Mathematics |
| url | http://psasir.upm.edu.my/id/eprint/114421/ http://psasir.upm.edu.my/id/eprint/114421/ http://psasir.upm.edu.my/id/eprint/114421/ http://psasir.upm.edu.my/id/eprint/114421/1/114421.pdf |