Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative
In this paper, we study a Volterra–Fredholm integro-differential equation. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of the Banach principle. Then, another result that deal...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5623388 |
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| author | Ameth Ndiaye Fulgence Mansal |
| author_facet | Ameth Ndiaye Fulgence Mansal |
| author_sort | Ameth Ndiaye |
| collection | DOAJ |
| description | In this paper, we study a Volterra–Fredholm integro-differential equation. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of the Banach principle. Then, another result that deals with the existence of at least one solution is delivered, and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. Ulam stability of the solution is discussed before including an example to illustrate the results of the proposal. |
| format | Article |
| id | doaj-art-39c034494a9745feb7c99f7c94910189 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-39c034494a9745feb7c99f7c949101892025-02-03T07:23:55ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/56233885623388Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional DerivativeAmeth Ndiaye0Fulgence Mansal1Département de Mathématiques, FASTEF, UCAD, Dakar, SenegalDépartement de Mathématiques et Informatique, UCAO, Dakar, SenegalIn this paper, we study a Volterra–Fredholm integro-differential equation. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of the Banach principle. Then, another result that deals with the existence of at least one solution is delivered, and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. Ulam stability of the solution is discussed before including an example to illustrate the results of the proposal.http://dx.doi.org/10.1155/2021/5623388 |
| spellingShingle | Ameth Ndiaye Fulgence Mansal Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative Journal of Mathematics |
| title | Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative |
| title_full | Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative |
| title_fullStr | Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative |
| title_full_unstemmed | Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative |
| title_short | Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative |
| title_sort | existence and uniqueness results of volterra fredholm integro differential equations via caputo fractional derivative |
| url | http://dx.doi.org/10.1155/2021/5623388 |
| work_keys_str_mv | AT amethndiaye existenceanduniquenessresultsofvolterrafredholmintegrodifferentialequationsviacaputofractionalderivative AT fulgencemansal existenceanduniquenessresultsofvolterrafredholmintegrodifferentialequationsviacaputofractionalderivative |