$Numerical methods for fractional differential equations by new caputo and hadamard types operators$

Numerical methods for fractional differential equations by new caputo and hadamard types operators

Fractional ordinary differential equation (FODE) and fractional partial differential equation (FPDE) emerges in various modelling of physics phenomena. Over past decades, several fractional derivative and operator has been introduced such as Caputo-Fabrizio operator, Caputo-Hadamard fractional...

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Main Author:	Toh, Yoke Teng
Format:	Thesis
Language:	English English English
Published:	2020
Subjects:	QA273-280 Probabilities Mathematical statistics
Online Access:	http://eprints.uthm.edu.my/957/1/24p%20TOH%20YOKE%20TENG.pdf http://eprints.uthm.edu.my/957/2/TOH%20YOKE%20TENG%20COPYRIGHT%20DECLARATION.pdf http://eprints.uthm.edu.my/957/3/TOH%20YOKE%20TENG%20WATERMARK.pdf
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id	my-uthm-ep.957
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spelling	my-uthm-ep.9572021-09-09T07:12:18Z Numerical methods for fractional differential equations by new caputo and hadamard types operators 2020-09 Toh, Yoke Teng QA273-280 Probabilities. Mathematical statistics Fractional ordinary differential equation (FODE) and fractional partial differential equation (FPDE) emerges in various modelling of physics phenomena. Over past decades, several fractional derivative and operator has been introduced such as Caputo-Fabrizio operator, Caputo-Hadamard fractional derivative, Marchaud fractional derivative or Caputo fractional derivative. The fractional differential equations defined in these fractional derivatives and operators definition are difficult or impossible to solve analytically. Therefore, we seek after highly accurate numerical scheme in efficient ways such as predictor-corrector method, finite difference scheme and spectral collocation method in this research for FODE and FPDE. Caputo-Fabrizo operator is a definition which is verified that does not fit the usual concept neither for fractional nor for integer derivative integral. The main interest of this operator is having regular kernel and which is a necessity of using a model describing the behavior of classical viscoelastic materials, electromagnetic system and viscoelastic materials. Furthermore, associated integral for Caputo�Fabrizio operator is also presented using Laplace transform and Inverse Laplace transform. Hence, we first introduce predictor-corrector scheme involving Caputo�Fabrizo operator, α > 0 which represents higher order of approximation 2020-09 Thesis http://eprints.uthm.edu.my/957/ http://eprints.uthm.edu.my/957/1/24p%20TOH%20YOKE%20TENG.pdf text en public http://eprints.uthm.edu.my/957/2/TOH%20YOKE%20TENG%20COPYRIGHT%20DECLARATION.pdf text en staffonly http://eprints.uthm.edu.my/957/3/TOH%20YOKE%20TENG%20WATERMARK.pdf text en validuser phd doctoral Universiti Tun Hussein Onn Malaysia Fakulti Sains Gunaan dan Teknologi
institution	Universiti Tun Hussein Onn Malaysia
collection	UTHM Institutional Repository
language	English English English
topic	QA273-280 Probabilities Mathematical statistics
spellingShingle	QA273-280 Probabilities Mathematical statistics Toh, Yoke Teng Numerical methods for fractional differential equations by new caputo and hadamard types operators
description	Fractional ordinary differential equation (FODE) and fractional partial differential equation (FPDE) emerges in various modelling of physics phenomena. Over past decades, several fractional derivative and operator has been introduced such as Caputo-Fabrizio operator, Caputo-Hadamard fractional derivative, Marchaud fractional derivative or Caputo fractional derivative. The fractional differential equations defined in these fractional derivatives and operators definition are difficult or impossible to solve analytically. Therefore, we seek after highly accurate numerical scheme in efficient ways such as predictor-corrector method, finite difference scheme and spectral collocation method in this research for FODE and FPDE. Caputo-Fabrizo operator is a definition which is verified that does not fit the usual concept neither for fractional nor for integer derivative integral. The main interest of this operator is having regular kernel and which is a necessity of using a model describing the behavior of classical viscoelastic materials, electromagnetic system and viscoelastic materials. Furthermore, associated integral for Caputo�Fabrizio operator is also presented using Laplace transform and Inverse Laplace transform. Hence, we first introduce predictor-corrector scheme involving Caputo�Fabrizo operator, α > 0 which represents higher order of approximation
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Toh, Yoke Teng
author_facet	Toh, Yoke Teng
author_sort	Toh, Yoke Teng
title	Numerical methods for fractional differential equations by new caputo and hadamard types operators
title_short	Numerical methods for fractional differential equations by new caputo and hadamard types operators
title_full	Numerical methods for fractional differential equations by new caputo and hadamard types operators
title_fullStr	Numerical methods for fractional differential equations by new caputo and hadamard types operators
title_full_unstemmed	Numerical methods for fractional differential equations by new caputo and hadamard types operators
title_sort	numerical methods for fractional differential equations by new caputo and hadamard types operators
granting_institution	Universiti Tun Hussein Onn Malaysia
granting_department	Fakulti Sains Gunaan dan Teknologi
publishDate	2020
url	http://eprints.uthm.edu.my/957/1/24p%20TOH%20YOKE%20TENG.pdf http://eprints.uthm.edu.my/957/2/TOH%20YOKE%20TENG%20COPYRIGHT%20DECLARATION.pdf http://eprints.uthm.edu.my/957/3/TOH%20YOKE%20TENG%20WATERMARK.pdf
_version_	1747830721171423232

Numerical methods for fractional differential equations by new caputo and hadamard types operators

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