Solutions of a Nonlinear Diffusion Equation with a Regularized Hyper-Bessel Operator
We investigate the Cauchy problem for a nonlinear fractional diffusion equation, which is modified using the time-fractional hyper-Bessel derivative. The source function is a gradient source of Hamilton–Jacobi type. The main objective of our current work is to show the existence and uniqueness of mi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/9/530 |
| _version_ | 1797488164443521024 |
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| author | Nguyen Hoang Luc Donal O’Regan Anh Tuan Nguyen |
| author_facet | Nguyen Hoang Luc Donal O’Regan Anh Tuan Nguyen |
| author_sort | Nguyen Hoang Luc |
| collection | DOAJ |
| description | We investigate the Cauchy problem for a nonlinear fractional diffusion equation, which is modified using the time-fractional hyper-Bessel derivative. The source function is a gradient source of Hamilton–Jacobi type. The main objective of our current work is to show the existence and uniqueness of mild solutions. Our desired goal is achieved using the Picard iteration method, and our analysis is based on properties of Mittag–Leffler functions and embeddings between Hilbert scales spaces and Lebesgue spaces. |
| first_indexed | 2024-03-09T23:58:10Z |
| format | Article |
| id | doaj.art-31702033a25647818966258d4c723bd8 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T23:58:10Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-31702033a25647818966258d4c723bd82023-11-23T16:20:13ZengMDPI AGFractal and Fractional2504-31102022-09-016953010.3390/fractalfract6090530Solutions of a Nonlinear Diffusion Equation with a Regularized Hyper-Bessel OperatorNguyen Hoang Luc0Donal O’Regan1Anh Tuan Nguyen2Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot City 75000, VietnamSchool of Mathematical and Statistical Sciences, National University of Ireland, H91 TK33 Galway, IrelandDivision of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot City 75000, VietnamWe investigate the Cauchy problem for a nonlinear fractional diffusion equation, which is modified using the time-fractional hyper-Bessel derivative. The source function is a gradient source of Hamilton–Jacobi type. The main objective of our current work is to show the existence and uniqueness of mild solutions. Our desired goal is achieved using the Picard iteration method, and our analysis is based on properties of Mittag–Leffler functions and embeddings between Hilbert scales spaces and Lebesgue spaces.https://www.mdpi.com/2504-3110/6/9/530gradient nonlinearityfractional diffusion equationhyper-Besselfractional partial differential equations |
| spellingShingle | Nguyen Hoang Luc Donal O’Regan Anh Tuan Nguyen Solutions of a Nonlinear Diffusion Equation with a Regularized Hyper-Bessel Operator Fractal and Fractional gradient nonlinearity fractional diffusion equation hyper-Bessel fractional partial differential equations |
| title | Solutions of a Nonlinear Diffusion Equation with a Regularized Hyper-Bessel Operator |
| title_full | Solutions of a Nonlinear Diffusion Equation with a Regularized Hyper-Bessel Operator |
| title_fullStr | Solutions of a Nonlinear Diffusion Equation with a Regularized Hyper-Bessel Operator |
| title_full_unstemmed | Solutions of a Nonlinear Diffusion Equation with a Regularized Hyper-Bessel Operator |
| title_short | Solutions of a Nonlinear Diffusion Equation with a Regularized Hyper-Bessel Operator |
| title_sort | solutions of a nonlinear diffusion equation with a regularized hyper bessel operator |
| topic | gradient nonlinearity fractional diffusion equation hyper-Bessel fractional partial differential equations |
| url | https://www.mdpi.com/2504-3110/6/9/530 |
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