Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problems
In this paper, we study an extension of Riemann–Liouville fractional derivative for a class of Riemann integrable functions to Lebesgue measurable and integrable functions. Then we used this extension for the approximate solution of a particular fractional partial differential equation (FPDE) proble...
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2018-10-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_24668_7f77da3165d7986d33973d6c90ccd7b4.pdf |
| _version_ | 1818411274634002432 |
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| author | S. Soradi Zeid A. V. Kamyad S. Effati |
| author_facet | S. Soradi Zeid A. V. Kamyad S. Effati |
| author_sort | S. Soradi Zeid |
| collection | DOAJ |
| description | In this paper, we study an extension of Riemann–Liouville fractional derivative for a class of Riemann integrable functions to Lebesgue measurable and integrable functions. Then we used this extension for the approximate solution of a particular fractional partial differential equation (FPDE) problems (linear space-time fractional order diffusion problems). To solve this problem, we reduce it approximately to a discrete optimization problem. Then, by using partition of measurable subsets of the domain of the original problem, we obtain some approximating solutions for it which are represented with acceptable accuracy. Indeed, by obtaining the suboptimal solutions of this optimization problem, we obtain the approximate solutions of the original problem. We show the efficiency of our approach by solving some numerical examples. |
| first_indexed | 2024-12-14T10:28:49Z |
| format | Article |
| id | doaj.art-1a4c3200b8af4714a95325d0f4b05c16 |
| institution | Directory Open Access Journal |
| issn | 2423-6977 2423-6969 |
| language | English |
| last_indexed | 2024-12-14T10:28:49Z |
| publishDate | 2018-10-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj.art-1a4c3200b8af4714a95325d0f4b05c162022-12-21T23:06:14ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692018-10-018212410.22067/ijnao.v8i2.5496224668Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problemsS. Soradi Zeid0A. V. Kamyad1S. Effati2Ferdowsi University of MashhadFerdowsi University of MashhadFerdowsi University of MashhadIn this paper, we study an extension of Riemann–Liouville fractional derivative for a class of Riemann integrable functions to Lebesgue measurable and integrable functions. Then we used this extension for the approximate solution of a particular fractional partial differential equation (FPDE) problems (linear space-time fractional order diffusion problems). To solve this problem, we reduce it approximately to a discrete optimization problem. Then, by using partition of measurable subsets of the domain of the original problem, we obtain some approximating solutions for it which are represented with acceptable accuracy. Indeed, by obtaining the suboptimal solutions of this optimization problem, we obtain the approximate solutions of the original problem. We show the efficiency of our approach by solving some numerical examples.https://ijnao.um.ac.ir/article_24668_7f77da3165d7986d33973d6c90ccd7b4.pdfriemann–liouville derivativefractional differential equationfractional partial differential equationlebesgue measurable and integrable function |
| spellingShingle | S. Soradi Zeid A. V. Kamyad S. Effati Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problems Iranian Journal of Numerical Analysis and Optimization riemann–liouville derivative fractional differential equation fractional partial differential equation lebesgue measurable and integrable function |
| title | Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problems |
| title_full | Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problems |
| title_fullStr | Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problems |
| title_full_unstemmed | Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problems |
| title_short | Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problems |
| title_sort | measurable functions approach for approximate solutions of linear space time fractional diffusion problems |
| topic | riemann–liouville derivative fractional differential equation fractional partial differential equation lebesgue measurable and integrable function |
| url | https://ijnao.um.ac.ir/article_24668_7f77da3165d7986d33973d6c90ccd7b4.pdf |
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