Fundamental Results about the Fractional Integro-Differential Equation Described with Caputo Derivative
In this paper, we study the existence and uniqueness of the mild solution of the fractional integro-differential with the nonlocal initial condition described by the Caputo fractional operator. Note that here the order of the Caputo derivative satisfies the condition that α∈1,2. The existence of α-r...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/9174488 |
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| author | Ndolane Sene |
| author_facet | Ndolane Sene |
| author_sort | Ndolane Sene |
| collection | DOAJ |
| description | In this paper, we study the existence and uniqueness of the mild solution of the fractional integro-differential with the nonlocal initial condition described by the Caputo fractional operator. Note that here the order of the Caputo derivative satisfies the condition that α∈1,2. The existence of α-resolvent operator in Banach space and fixed point theorem has been utilized in the proof of the existence of the mild solution. We have established in this paper the Hyers-Ulam stability of the mild solution of the considered fractional integro-differential equation. An illustrative example has been provided to support the main findings of the paper. |
| format | Article |
| id | doaj-art-8131c57e03d24b629f804a9ecdd5d447 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-8131c57e03d24b629f804a9ecdd5d4472025-02-03T01:08:46ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/9174488Fundamental Results about the Fractional Integro-Differential Equation Described with Caputo DerivativeNdolane Sene0Department of MathematicsIn this paper, we study the existence and uniqueness of the mild solution of the fractional integro-differential with the nonlocal initial condition described by the Caputo fractional operator. Note that here the order of the Caputo derivative satisfies the condition that α∈1,2. The existence of α-resolvent operator in Banach space and fixed point theorem has been utilized in the proof of the existence of the mild solution. We have established in this paper the Hyers-Ulam stability of the mild solution of the considered fractional integro-differential equation. An illustrative example has been provided to support the main findings of the paper.http://dx.doi.org/10.1155/2022/9174488 |
| spellingShingle | Ndolane Sene Fundamental Results about the Fractional Integro-Differential Equation Described with Caputo Derivative Journal of Function Spaces |
| title | Fundamental Results about the Fractional Integro-Differential Equation Described with Caputo Derivative |
| title_full | Fundamental Results about the Fractional Integro-Differential Equation Described with Caputo Derivative |
| title_fullStr | Fundamental Results about the Fractional Integro-Differential Equation Described with Caputo Derivative |
| title_full_unstemmed | Fundamental Results about the Fractional Integro-Differential Equation Described with Caputo Derivative |
| title_short | Fundamental Results about the Fractional Integro-Differential Equation Described with Caputo Derivative |
| title_sort | fundamental results about the fractional integro differential equation described with caputo derivative |
| url | http://dx.doi.org/10.1155/2022/9174488 |
| work_keys_str_mv | AT ndolanesene fundamentalresultsaboutthefractionalintegrodifferentialequationdescribedwithcaputoderivative |