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
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spelling	my-usm-ep.602722024-03-25T07:16:48Z Residual Methods For Solving Fractional Differential Equations With Singular Kernels 2023-01 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 http://eprints.usm.my/60272/ http://eprints.usm.my/60272/1/Pages%20from%20MOHAMMED%20M.%20A.%20ABUOMAR%20-%20TESIS-2.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik ( School of Mathematical Sciences)
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
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
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
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
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Sains Matematik ( School of Mathematical Sciences)
publishDate	2023
url	http://eprints.usm.my/60272/1/Pages%20from%20MOHAMMED%20M.%20A.%20ABUOMAR%20-%20TESIS-2.pdf
_version_	1804888903183761408

Residual Methods For Solving Fractional Differential Equations With Singular Kernels

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