Analyzing inverse backward problem in nonlinear integro-differential equation with memory kernel
This paper focuses on the backward problem related to an integro-differential equation with a general convolutional derivative in time and nonlinear source terms. The existence, uniqueness, and regularity of the mild solution to the proposed problem are established under certain assumptions in a sui...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-11-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037424000876 |
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| author | M.J. Huntul |
| author_facet | M.J. Huntul |
| author_sort | M.J. Huntul |
| collection | DOAJ |
| description | This paper focuses on the backward problem related to an integro-differential equation with a general convolutional derivative in time and nonlinear source terms. The existence, uniqueness, and regularity of the mild solution to the proposed problem are established under certain assumptions in a suitable space. The proposed problem is ill-posed in the sense of Hadamard. Moreover, the Fourier truncation method is used to construct a regularized solution. Finally, the convergence rate between the regularized solution and the exact solution is determined. |
| format | Article |
| id | doaj-art-4c44af4a45b24c50b572e45500ff6b21 |
| institution | DOAJ |
| issn | 2590-0374 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-4c44af4a45b24c50b572e45500ff6b212025-08-20T02:49:29ZengElsevierResults in Applied Mathematics2590-03742024-11-012410051710.1016/j.rinam.2024.100517Analyzing inverse backward problem in nonlinear integro-differential equation with memory kernelM.J. Huntul0Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Kingdom of Saudi ArabiaThis paper focuses on the backward problem related to an integro-differential equation with a general convolutional derivative in time and nonlinear source terms. The existence, uniqueness, and regularity of the mild solution to the proposed problem are established under certain assumptions in a suitable space. The proposed problem is ill-posed in the sense of Hadamard. Moreover, the Fourier truncation method is used to construct a regularized solution. Finally, the convergence rate between the regularized solution and the exact solution is determined.http://www.sciencedirect.com/science/article/pii/S2590037424000876Backward problemGeneralized fractional derivativesUnique existence and regularity resultsIll-posednessMittag-Leffler type functions |
| spellingShingle | M.J. Huntul Analyzing inverse backward problem in nonlinear integro-differential equation with memory kernel Results in Applied Mathematics Backward problem Generalized fractional derivatives Unique existence and regularity results Ill-posedness Mittag-Leffler type functions |
| title | Analyzing inverse backward problem in nonlinear integro-differential equation with memory kernel |
| title_full | Analyzing inverse backward problem in nonlinear integro-differential equation with memory kernel |
| title_fullStr | Analyzing inverse backward problem in nonlinear integro-differential equation with memory kernel |
| title_full_unstemmed | Analyzing inverse backward problem in nonlinear integro-differential equation with memory kernel |
| title_short | Analyzing inverse backward problem in nonlinear integro-differential equation with memory kernel |
| title_sort | analyzing inverse backward problem in nonlinear integro differential equation with memory kernel |
| topic | Backward problem Generalized fractional derivatives Unique existence and regularity results Ill-posedness Mittag-Leffler type functions |
| url | http://www.sciencedirect.com/science/article/pii/S2590037424000876 |
| work_keys_str_mv | AT mjhuntul analyzinginversebackwardprobleminnonlinearintegrodifferentialequationwithmemorykernel |