On Fractional Diffusion Equation with Caputo-Fabrizio Derivative and Memory Term
In this paper, we examine a nonlinear fractional diffusion equation containing viscosity terms with derivative in the sense of Caputo-Fabrizio. First, we establish the local existence and uniqueness of lightweight solutions under some assumptions about the input data. Then, we get the global solutio...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/9259967 |
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| _version_ | 1832561414680608768 |
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| author | Binh Duy Ho Van Kim Ho Thi Long Le Dinh Nguyen Hoang Luc Phuong Nguyen |
| author_facet | Binh Duy Ho Van Kim Ho Thi Long Le Dinh Nguyen Hoang Luc Phuong Nguyen |
| author_sort | Binh Duy Ho |
| collection | DOAJ |
| description | In this paper, we examine a nonlinear fractional diffusion equation containing viscosity terms with derivative in the sense of Caputo-Fabrizio. First, we establish the local existence and uniqueness of lightweight solutions under some assumptions about the input data. Then, we get the global solution using some new techniques. Our main idea is to combine theories of Banach’s fixed point theorem, Hilbert scale theory of space, and some Sobolev embedding. |
| format | Article |
| id | doaj-art-3103dde5090440958fbdba7be9e556ea |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-3103dde5090440958fbdba7be9e556ea2025-02-03T01:24:59ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/92599679259967On Fractional Diffusion Equation with Caputo-Fabrizio Derivative and Memory TermBinh Duy Ho0Van Kim Ho Thi1Long Le Dinh2Nguyen Hoang Luc3Phuong Nguyen4Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, VietnamDivision of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, VietnamDivision of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, VietnamDivision of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, VietnamFaculty of Fundamental Science, Industrial University of Ho Chi Minh City, VietnamIn this paper, we examine a nonlinear fractional diffusion equation containing viscosity terms with derivative in the sense of Caputo-Fabrizio. First, we establish the local existence and uniqueness of lightweight solutions under some assumptions about the input data. Then, we get the global solution using some new techniques. Our main idea is to combine theories of Banach’s fixed point theorem, Hilbert scale theory of space, and some Sobolev embedding.http://dx.doi.org/10.1155/2021/9259967 |
| spellingShingle | Binh Duy Ho Van Kim Ho Thi Long Le Dinh Nguyen Hoang Luc Phuong Nguyen On Fractional Diffusion Equation with Caputo-Fabrizio Derivative and Memory Term Advances in Mathematical Physics |
| title | On Fractional Diffusion Equation with Caputo-Fabrizio Derivative and Memory Term |
| title_full | On Fractional Diffusion Equation with Caputo-Fabrizio Derivative and Memory Term |
| title_fullStr | On Fractional Diffusion Equation with Caputo-Fabrizio Derivative and Memory Term |
| title_full_unstemmed | On Fractional Diffusion Equation with Caputo-Fabrizio Derivative and Memory Term |
| title_short | On Fractional Diffusion Equation with Caputo-Fabrizio Derivative and Memory Term |
| title_sort | on fractional diffusion equation with caputo fabrizio derivative and memory term |
| url | http://dx.doi.org/10.1155/2021/9259967 |
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