$Efficient schemes on solving fractional integro-differential equations$

Efficient schemes on solving fractional integro-differential equations

Fractional integro-differential equation (FIDE) emerges in various modelling of physical phenomena. In most cases, finding the exact analytical solution for FIDE is difficult or not possible. Hence, the methods producing highly accurate numerical solution in efficient ways are often sought after....

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Main Author:	Loh, Jian Rong
Format:	Thesis
Language:	English English English
Published:	2018
Subjects:	QA Mathematics
Online Access:	http://eprints.uthm.edu.my/204/1/LOH%20JIAN%20RONG%20COPYRIGHT%20DECLARATION.pdf http://eprints.uthm.edu.my/204/2/LOH%20JIAN%20RONG%20WATERMARK.pdf http://eprints.uthm.edu.my/204/3/24p%20LOH%20JIAN%20RONG.pdf
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spelling	my-uthm-ep.2042021-07-06T08:22:08Z Efficient schemes on solving fractional integro-differential equations 2018-02 Loh, Jian Rong QA Mathematics Fractional integro-differential equation (FIDE) emerges in various modelling of physical phenomena. In most cases, finding the exact analytical solution for FIDE is difficult or not possible. Hence, the methods producing highly accurate numerical solution in efficient ways are often sought after. This research has designed some methods to find the approximate solution of FIDE. The analytical expression of Genocchi polynomial operational matrix for left-sided and right-sided Caputo’s derivative and kernel matrix has been derived. Linear independence of Genocchi polynomials has been proved by deriving the expression for Genocchi polynomial Gram determinant. Genocchi polynomial method with collocation has been introduced and applied in solving both linear and system of linear FIDE. The numerical results of solving linear FIDE by Genocchi polynomial are compared with certain existing methods. The analytical expression of Bernoulli polynomial operational matrix of right-sided Caputo’s fractional derivative and the Bernoulli expansion coefficient for a two-variable function is derived. Linear FIDE with mixed left and right-sided Caputo’s derivative is first considered and solved by applying the Bernoulli polynomial with spectral-tau method. Numerical results obtained show that the method proposed achieves very high accuracy. The upper bounds for the 2018-02 Thesis http://eprints.uthm.edu.my/204/ http://eprints.uthm.edu.my/204/1/LOH%20JIAN%20RONG%20COPYRIGHT%20DECLARATION.pdf text en staffonly http://eprints.uthm.edu.my/204/2/LOH%20JIAN%20RONG%20WATERMARK.pdf text en validuser http://eprints.uthm.edu.my/204/3/24p%20LOH%20JIAN%20RONG.pdf text en public 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	QA Mathematics
spellingShingle	QA Mathematics Loh, Jian Rong Efficient schemes on solving fractional integro-differential equations
description	Fractional integro-differential equation (FIDE) emerges in various modelling of physical phenomena. In most cases, finding the exact analytical solution for FIDE is difficult or not possible. Hence, the methods producing highly accurate numerical solution in efficient ways are often sought after. This research has designed some methods to find the approximate solution of FIDE. The analytical expression of Genocchi polynomial operational matrix for left-sided and right-sided Caputo’s derivative and kernel matrix has been derived. Linear independence of Genocchi polynomials has been proved by deriving the expression for Genocchi polynomial Gram determinant. Genocchi polynomial method with collocation has been introduced and applied in solving both linear and system of linear FIDE. The numerical results of solving linear FIDE by Genocchi polynomial are compared with certain existing methods. The analytical expression of Bernoulli polynomial operational matrix of right-sided Caputo’s fractional derivative and the Bernoulli expansion coefficient for a two-variable function is derived. Linear FIDE with mixed left and right-sided Caputo’s derivative is first considered and solved by applying the Bernoulli polynomial with spectral-tau method. Numerical results obtained show that the method proposed achieves very high accuracy. The upper bounds for the
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Loh, Jian Rong
author_facet	Loh, Jian Rong
author_sort	Loh, Jian Rong
title	Efficient schemes on solving fractional integro-differential equations
title_short	Efficient schemes on solving fractional integro-differential equations
title_full	Efficient schemes on solving fractional integro-differential equations
title_fullStr	Efficient schemes on solving fractional integro-differential equations
title_full_unstemmed	Efficient schemes on solving fractional integro-differential equations
title_sort	efficient schemes on solving fractional integro-differential equations
granting_institution	Universiti Tun Hussein Onn Malaysia
granting_department	Fakulti Sains Gunaan dan Teknologi
publishDate	2018
url	http://eprints.uthm.edu.my/204/1/LOH%20JIAN%20RONG%20COPYRIGHT%20DECLARATION.pdf http://eprints.uthm.edu.my/204/2/LOH%20JIAN%20RONG%20WATERMARK.pdf http://eprints.uthm.edu.my/204/3/24p%20LOH%20JIAN%20RONG.pdf
_version_	1747830553281822720

Efficient schemes on solving fractional integro-differential equations

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