$Numerical solution for fractionalorder logistic equation$

Numerical solution for fractionalorder logistic equation

Recently, in the direction of developing realistic mathematical models, there are a number of works that extended the ordinary differential equation to the fractionalorder equation. Fractional-order models are thought to provide better agreement with the real data compared with th...

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Main Author:	Kaharuddin, Liyana Nadhira
Format:	Thesis
Language:	English English English
Published:	2021
Subjects:	QA273-280 Probabilities Mathematical statistics
Online Access:	http://eprints.uthm.edu.my/6293/1/24p%20LIYANA%20NADHIRA%20KAHARUDDIN.pdf http://eprints.uthm.edu.my/6293/2/LIYANA%20NADHIRA%20KAHARUDDIN%20COPYRIGHT%20DECLARATION.pdf http://eprints.uthm.edu.my/6293/3/LIYANA%20NADHIRA%20KAHARUDDIN%20WATERMARK.pdf
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spelling	my-uthm-ep.62932022-02-05T07:20:05Z Numerical solution for fractionalorder logistic equation 2021-04 Kaharuddin, Liyana Nadhira QA273-280 Probabilities. Mathematical statistics Recently, in the direction of developing realistic mathematical models, there are a number of works that extended the ordinary differential equation to the fractionalorder equation. Fractional-order models are thought to provide better agreement with the real data compared with the integer-order models. The fractional logistic equation is one of the equations that has been getting the attention of researchers due to its nature in predicting population growth and studying growth trends, which assists in decision making and future planning. This research aims to propose the numerical solution for the fractional logistic equation. Two different solving methods, which are the Adam’s-type predictor-corrector method and the Q-modified Eulerian numbers, were successfully applied to two versions of the fractional-order logistic equation, which are the fractional modified logistic equation and the fractional logistic equation, respectively. The fractional modified logistic equation, which involved the extended Monod model, was solved by the Adam’s-type predictor-corrector method and was applied in estimating microalgae growth. The results show that the fractional modified logistic equation agreed with the real data of microalgae growth. Meanwhile, a closedform solution by the Q-modified Eulerian numbers was proposed for the fractional logistic equation. These modified Eulerian numbers were obtained by modifying the Eulerian polynomials in two variables. Interestingly, these modified polynomials corresponded to the polylogarithm p Li z( ) of the negative order and with a negative real argument, z . The proposed method via the modified Eulerian numbers can provide the generalised solution for an arbitrary value. The proposed method was shown to achieve numerical convergence. The numerical experiment shows that this method is highly efficient and accurate since the absolute error obtained from the subtraction of the exact and proposed solution is considerably small. 2021-04 Thesis http://eprints.uthm.edu.my/6293/ http://eprints.uthm.edu.my/6293/1/24p%20LIYANA%20NADHIRA%20KAHARUDDIN.pdf text en public http://eprints.uthm.edu.my/6293/2/LIYANA%20NADHIRA%20KAHARUDDIN%20COPYRIGHT%20DECLARATION.pdf text en staffonly http://eprints.uthm.edu.my/6293/3/LIYANA%20NADHIRA%20KAHARUDDIN%20WATERMARK.pdf text en validuser mphil masters Universiti Tun Hussein 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 Kaharuddin, Liyana Nadhira Numerical solution for fractionalorder logistic equation
description	Recently, in the direction of developing realistic mathematical models, there are a number of works that extended the ordinary differential equation to the fractionalorder equation. Fractional-order models are thought to provide better agreement with the real data compared with the integer-order models. The fractional logistic equation is one of the equations that has been getting the attention of researchers due to its nature in predicting population growth and studying growth trends, which assists in decision making and future planning. This research aims to propose the numerical solution for the fractional logistic equation. Two different solving methods, which are the Adam’s-type predictor-corrector method and the Q-modified Eulerian numbers, were successfully applied to two versions of the fractional-order logistic equation, which are the fractional modified logistic equation and the fractional logistic equation, respectively. The fractional modified logistic equation, which involved the extended Monod model, was solved by the Adam’s-type predictor-corrector method and was applied in estimating microalgae growth. The results show that the fractional modified logistic equation agreed with the real data of microalgae growth. Meanwhile, a closedform solution by the Q-modified Eulerian numbers was proposed for the fractional logistic equation. These modified Eulerian numbers were obtained by modifying the Eulerian polynomials in two variables. Interestingly, these modified polynomials corresponded to the polylogarithm p Li z( ) of the negative order and with a negative real argument, z . The proposed method via the modified Eulerian numbers can provide the generalised solution for an arbitrary value. The proposed method was shown to achieve numerical convergence. The numerical experiment shows that this method is highly efficient and accurate since the absolute error obtained from the subtraction of the exact and proposed solution is considerably small.
format	Thesis
qualification_name	Master of Philosophy (M.Phil.)
qualification_level	Master's degree
author	Kaharuddin, Liyana Nadhira
author_facet	Kaharuddin, Liyana Nadhira
author_sort	Kaharuddin, Liyana Nadhira
title	Numerical solution for fractionalorder logistic equation
title_short	Numerical solution for fractionalorder logistic equation
title_full	Numerical solution for fractionalorder logistic equation
title_fullStr	Numerical solution for fractionalorder logistic equation
title_full_unstemmed	Numerical solution for fractionalorder logistic equation
title_sort	numerical solution for fractionalorder logistic equation
granting_institution	Universiti Tun Hussein Malaysia
granting_department	Fakulti Sains Gunaan dan Teknologi
publishDate	2021
url	http://eprints.uthm.edu.my/6293/1/24p%20LIYANA%20NADHIRA%20KAHARUDDIN.pdf http://eprints.uthm.edu.my/6293/2/LIYANA%20NADHIRA%20KAHARUDDIN%20COPYRIGHT%20DECLARATION.pdf http://eprints.uthm.edu.my/6293/3/LIYANA%20NADHIRA%20KAHARUDDIN%20WATERMARK.pdf
_version_	1747831061281243136

Numerical solution for fractionalorder logistic equation

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