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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主要作者: Toh, Yoke Teng
格式: Thesis
语言:English
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出版: 2020
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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
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