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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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Main Author: Abuomar, Mohammed M. A.
Format: Thesis
Language:English
Published: 2023
Subjects:
QA1 Mathematics (General)
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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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.
institution Universiti Sains Malaysia
building Hamzah Sendut Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Sains Malaysia
content_source USM Institutional Repository
url_provider http://eprints.usm.my/
language English
topic QA1 Mathematics (General)
spellingShingle QA1 Mathematics (General)
Abuomar, Mohammed M. A.
Residual Methods For Solving Fractional Differential Equations With Singular Kernels
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
author Abuomar, Mohammed M. A.
author_facet Abuomar, Mohammed M. A.
author_sort Abuomar, Mohammed M. A.
title Residual Methods For Solving Fractional Differential Equations With Singular Kernels
title_short 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_sort residual methods for solving fractional differential equations with singular kernels
publishDate 2023
url http://eprints.usm.my/60272/1/Pages%20from%20MOHAMMED%20M.%20A.%20ABUOMAR%20-%20TESIS-2.pdf
http://eprints.usm.my/60272/
_version_ 1794634924510150656
score 13.160551

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