Residual Methods For Solving Fractional Differential Equations With Singular Kernels
In this thesis, we implement two residual methods to solve two important fractional applications in science and engineering. The fractional derivative is used in the Caputo sense. For this reason, we start this study by discussing and providing several properties of fractional calculus. Comprehensiv...
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| Format: | Thesis |
| Language: | en |
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2023
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| Online Access: | http://eprints.usm.my/60272/1/Pages%20from%20MOHAMMED%20M.%20A.%20ABUOMAR%20-%20TESIS-2.pdf http://eprints.usm.my/60272/ |
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| _version_ | 1834507312323100672 |
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| author | Abuomar, Mohammed M. A. |
| author_facet | Abuomar, Mohammed M. A. |
| author_sort | Abuomar, Mohammed M. A. |
| building | Hamzah Sendut Library |
| collection | Institutional Repository |
| content_provider | Universiti Sains Malaysia |
| content_source | USM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | In this thesis, we implement two residual methods to solve two important fractional applications in science and engineering. The fractional derivative is used in the Caputo sense. For this reason, we start this study by discussing and providing several properties of fractional calculus. Comprehensive study for the theory of fractional calculus are presented. The first residual method used in this thesis is a combination of fractional series method and fractional Laplace transform method. This combination is use to solve an important application in physics which is the fractional diffusion-wave equation with a reaction. The main purpose of this method is to solve this problem analytically. |
| format | Thesis |
| id | my.usm.eprints.60272 |
| institution | Universiti Sains Malaysia |
| language | en |
| publishDate | 2023 |
| record_format | eprints |
| spelling | my.usm.eprints.60272 http://eprints.usm.my/60272/ Residual Methods For Solving Fractional Differential Equations With Singular Kernels Abuomar, Mohammed M. A. QA1 Mathematics (General) In this thesis, we implement two residual methods to solve two important fractional applications in science and engineering. The fractional derivative is used in the Caputo sense. For this reason, we start this study by discussing and providing several properties of fractional calculus. Comprehensive study for the theory of fractional calculus are presented. The first residual method used in this thesis is a combination of fractional series method and fractional Laplace transform method. This combination is use to solve an important application in physics which is the fractional diffusion-wave equation with a reaction. The main purpose of this method is to solve this problem analytically. 2023-01 Thesis NonPeerReviewed application/pdf en http://eprints.usm.my/60272/1/Pages%20from%20MOHAMMED%20M.%20A.%20ABUOMAR%20-%20TESIS-2.pdf Abuomar, Mohammed M. A. (2023) Residual Methods For Solving Fractional Differential Equations With Singular Kernels. PhD thesis, Universiti Sains Malaysia. |
| spellingShingle | QA1 Mathematics (General) Abuomar, Mohammed M. A. Residual Methods For Solving Fractional Differential Equations With Singular Kernels |
| title | Residual Methods For Solving Fractional Differential Equations With Singular Kernels |
| title_full | Residual Methods For Solving Fractional Differential Equations With Singular Kernels |
| title_fullStr | Residual Methods For Solving Fractional Differential Equations With Singular Kernels |
| title_full_unstemmed | Residual Methods For Solving Fractional Differential Equations With Singular Kernels |
| title_short | Residual Methods For Solving Fractional Differential Equations With Singular Kernels |
| title_sort | residual methods for solving fractional differential equations with singular kernels |
| topic | QA1 Mathematics (General) |
| url | http://eprints.usm.my/60272/1/Pages%20from%20MOHAMMED%20M.%20A.%20ABUOMAR%20-%20TESIS-2.pdf http://eprints.usm.my/60272/ |
| url_provider | http://eprints.usm.my/ |