$Wavelets operational methods for fractional differential equations and systems of fractional differential equations$

Wavelets operational methods for fractional differential equations and systems of fractional differential equations

In this thesis, new and effective operational methods based on polynomials and wavelets for the solutions of FDEs and systems of FDEs are developed. In particular we study one of the important polynomial that belongs to the Appell family of polynomials, namely, Genocchi polynomial. This polynomia...

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Main Author:	Isah, Abdulnasir
Format:	Thesis
Language:	English English
Published:	2017
Subjects:	QA273-280 Probabilities Mathematical statistics
Online Access:	http://eprints.uthm.edu.my/291/1/24p%20ABDULNASIR%20ISAH.pdf http://eprints.uthm.edu.my/291/2/ABDULNASIR%20ISAH%20WATERMARK.pdf
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spelling	my-uthm-ep.2912021-07-21T02:39:53Z Wavelets operational methods for fractional differential equations and systems of fractional differential equations 2017-02 Isah, Abdulnasir QA273-280 Probabilities. Mathematical statistics In this thesis, new and effective operational methods based on polynomials and wavelets for the solutions of FDEs and systems of FDEs are developed. In particular we study one of the important polynomial that belongs to the Appell family of polynomials, namely, Genocchi polynomial. This polynomial has certain great advantages based on which an effective and simple operational matrix of derivative was first derived and applied together with collocation method to solve some singular second order differential equations of Emden-Fowler type, a class of generalized Pantograph equations and Delay differential systems. A new operational matrix of fractional order derivative and integration based on this polynomial was also developed and used together with collocation method to solve FDEs, systems of FDEs and fractional order delay differential equations. Error bound for some of the considered problems is also shown and proved. Further, a wavelet bases based on Genocchi polynomials is also constructed, its operational matrix of fractional order derivative is derived and used for the solutions of FDEs and systems of FDEs. A novel approach for obtaining operational matrices of fractional derivative based on Legendre and Chebyshev wavelets is developed, where, the wavelets are first transformed into corresponding shifted polynomials and the transformation matrices are formed and used together with the polynomials operational matrices of fractional derivatives to obtain the wavelets operational matrix. These new operational matrices are used together with spectral Tau and collocation methods to solve FDEs and systems of FDEs. 2017-02 Thesis http://eprints.uthm.edu.my/291/ http://eprints.uthm.edu.my/291/1/24p%20ABDULNASIR%20ISAH.pdf text en public http://eprints.uthm.edu.my/291/2/ABDULNASIR%20ISAH%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
topic	QA273-280 Probabilities Mathematical statistics
spellingShingle	QA273-280 Probabilities Mathematical statistics Isah, Abdulnasir Wavelets operational methods for fractional differential equations and systems of fractional differential equations
description	In this thesis, new and effective operational methods based on polynomials and wavelets for the solutions of FDEs and systems of FDEs are developed. In particular we study one of the important polynomial that belongs to the Appell family of polynomials, namely, Genocchi polynomial. This polynomial has certain great advantages based on which an effective and simple operational matrix of derivative was first derived and applied together with collocation method to solve some singular second order differential equations of Emden-Fowler type, a class of generalized Pantograph equations and Delay differential systems. A new operational matrix of fractional order derivative and integration based on this polynomial was also developed and used together with collocation method to solve FDEs, systems of FDEs and fractional order delay differential equations. Error bound for some of the considered problems is also shown and proved. Further, a wavelet bases based on Genocchi polynomials is also constructed, its operational matrix of fractional order derivative is derived and used for the solutions of FDEs and systems of FDEs. A novel approach for obtaining operational matrices of fractional derivative based on Legendre and Chebyshev wavelets is developed, where, the wavelets are first transformed into corresponding shifted polynomials and the transformation matrices are formed and used together with the polynomials operational matrices of fractional derivatives to obtain the wavelets operational matrix. These new operational matrices are used together with spectral Tau and collocation methods to solve FDEs and systems of FDEs.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Isah, Abdulnasir
author_facet	Isah, Abdulnasir
author_sort	Isah, Abdulnasir
title	Wavelets operational methods for fractional differential equations and systems of fractional differential equations
title_short	Wavelets operational methods for fractional differential equations and systems of fractional differential equations
title_full	Wavelets operational methods for fractional differential equations and systems of fractional differential equations
title_fullStr	Wavelets operational methods for fractional differential equations and systems of fractional differential equations
title_full_unstemmed	Wavelets operational methods for fractional differential equations and systems of fractional differential equations
title_sort	wavelets operational methods for fractional differential equations and systems of fractional differential equations
granting_institution	Universiti Tun Hussein Onn Malaysia
granting_department	Fakulti Sains Gunaan dan Teknologi
publishDate	2017
url	http://eprints.uthm.edu.my/291/1/24p%20ABDULNASIR%20ISAH.pdf http://eprints.uthm.edu.my/291/2/ABDULNASIR%20ISAH%20WATERMARK.pdf
_version_	1747830574704230400

Wavelets operational methods for fractional differential equations and systems of fractional differential equations

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