On Cauchy problem for pseudo-parabolic equation with Caputo-Fabrizio operator
In this article, we considered the pseudo-parabolic equation with Caputo-Fabrizio fractional derivative. This equation has many applications in different fields, such as science, technology, and so on. In this article, we gave the formula of mild solution, which is represented in the form of Fourier...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-01-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2022-0180 |
| _version_ | 1811171894817193984 |
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| author | Nghia Bui Dai Nguyen Van Tien Long Le Dinh |
| author_facet | Nghia Bui Dai Nguyen Van Tien Long Le Dinh |
| author_sort | Nghia Bui Dai |
| collection | DOAJ |
| description | In this article, we considered the pseudo-parabolic equation with Caputo-Fabrizio fractional derivative. This equation has many applications in different fields, such as science, technology, and so on. In this article, we gave the formula of mild solution, which is represented in the form of Fourier series by some operators . In the linear case, we investigated the continuity of the mild solution with respect to the fractional order. For the nonlinear case, we investigated the existence and uniqueness of a global solution. The main proof technique is based on the Banach fixed point theorem combined with some Sobolev embeddings. For more detailed, we obtained two other interesting results: the continuity of mild solution with respect to the derivative order and the convergence of solution as the coefficient k approaches to zero. |
| first_indexed | 2024-04-10T17:22:54Z |
| format | Article |
| id | doaj.art-9775d8985b40455db0df28b71f30ab98 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-04-10T17:22:54Z |
| publishDate | 2023-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-9775d8985b40455db0df28b71f30ab982023-02-05T08:30:37ZengDe GruyterDemonstratio Mathematica2391-46612023-01-0156131333310.1515/dema-2022-0180On Cauchy problem for pseudo-parabolic equation with Caputo-Fabrizio operatorNghia Bui Dai0Nguyen Van Tien1Long Le Dinh2Department of Mathematics, Faculty of Science, Nong Lam University, Ho Chi Minh City, VietnamFalculty of Maths, FPT University HCM, Saigon Hi-tech Park, Ho Chi Minh City, VietnamDivision of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, VietnamIn this article, we considered the pseudo-parabolic equation with Caputo-Fabrizio fractional derivative. This equation has many applications in different fields, such as science, technology, and so on. In this article, we gave the formula of mild solution, which is represented in the form of Fourier series by some operators . In the linear case, we investigated the continuity of the mild solution with respect to the fractional order. For the nonlinear case, we investigated the existence and uniqueness of a global solution. The main proof technique is based on the Banach fixed point theorem combined with some Sobolev embeddings. For more detailed, we obtained two other interesting results: the continuity of mild solution with respect to the derivative order and the convergence of solution as the coefficient k approaches to zero.https://doi.org/10.1515/dema-2022-0180caputo-fabrizio derivative operatorburger equationbanach fixed point theorysobolev embeddings35r1135b6526a33 |
| spellingShingle | Nghia Bui Dai Nguyen Van Tien Long Le Dinh On Cauchy problem for pseudo-parabolic equation with Caputo-Fabrizio operator Demonstratio Mathematica caputo-fabrizio derivative operator burger equation banach fixed point theory sobolev embeddings 35r11 35b65 26a33 |
| title | On Cauchy problem for pseudo-parabolic equation with Caputo-Fabrizio operator |
| title_full | On Cauchy problem for pseudo-parabolic equation with Caputo-Fabrizio operator |
| title_fullStr | On Cauchy problem for pseudo-parabolic equation with Caputo-Fabrizio operator |
| title_full_unstemmed | On Cauchy problem for pseudo-parabolic equation with Caputo-Fabrizio operator |
| title_short | On Cauchy problem for pseudo-parabolic equation with Caputo-Fabrizio operator |
| title_sort | on cauchy problem for pseudo parabolic equation with caputo fabrizio operator |
| topic | caputo-fabrizio derivative operator burger equation banach fixed point theory sobolev embeddings 35r11 35b65 26a33 |
| url | https://doi.org/10.1515/dema-2022-0180 |
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