Fuzzy Sumudu transform

Ordinary differential Equations (ODEs) have long been used to model real-life problems. As times goes on, researchers realized that ODEs are no longer the best modelling tool, since they are inaccurate, especially when dealing with stuff that are surrounded by uncertainties. To deal with this, resea...

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Format:	Thesis
Language:	English
Subjects:	Transformations (Mathematics) Differential equations Integral transforms Ordinary differential Equations (ODEs) Fuzzy Sumudu transform (FST) Fuzzy numbers
Online Access:	http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77980/1/Page%201-24.pdf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77980/2/Full%20text.pdf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77980/4/Norazrizal.pdf
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id	my-unimap-77980
record_format	uketd_dc
spelling	my-unimap-779802023-03-06T02:09:18Z Fuzzy Sumudu transform Muhammad Zaini, Ahmad, Dr. Ordinary differential Equations (ODEs) have long been used to model real-life problems. As times goes on, researchers realized that ODEs are no longer the best modelling tool, since they are inaccurate, especially when dealing with stuff that are surrounded by uncertainties. To deal with this, researchers utilized the fuzzy set theory to propose fuzzy differential equations (FDEs). Unlike ODEs which could not cope with uncertainties at the initial values, FDEs handle this efficiently. However, the methods that can be used to deal with FDEs are very limited, and many of them are still at development stages. In this research, a new analytical method is proposed for solving a class of FDEs, including FDEs of integer order, fuzzy fractional differential equations (FFDEs), fuzzy partial differential equations (FPDEs) and system of linear fuzzy differential equations (SLFDEs). For this purpose, a novel integral transform called fuzzy Sumudu transform (FST) is proposed. This is done by integrating the fuzzy set theory and the classical Sumudu transform (CST). New properties and fundamental results concerning FST are proposed and proved mathematically. These new properties comprised results on duality with fuzzy Laplace transform (FLT), linearity, preserving, shifting, convolution, as well as theorems for fuzzy derivatives. The proposed results are then used to construct detailed procedures for solving FDEs, FFDEs, FPDEs and SLFDEs where the class of FDEs are interpreted under the strongly generalized differentiability concept. From there, the procedures are demonstrated on some examples, in order to illustrate FST applicability. Some analyses are performed where the behaviour of the solutions obtained are described in particulars. Furthermore, a comparison between the solutions obtained for the class of FDEs are compared with the solutions obtained using ODEs, where the ODEs include integer order ODEs, fractional differential equations (FrDEs), partial differential equations (PDEs) and system of linear differential equations (SLDEs). The main advantage of FST highlighted in this thesis is that it possessed the scale preserving property. This means that the transformed function, with a new domain, is a similitude to the original function. Additionally, this research provides an alternative for researchers when dealing with the class of FDEs. Universiti Malaysia Perlis (UniMAP) Thesis en http://dspace.unimap.edu.my:80/xmlui/handle/123456789/77980 http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77980/3/license.txt 8a4605be74aa9ea9d79846c1fba20a33 http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77980/1/Page%201-24.pdf 4c5ed7ab460cd6ed398391c5114dcfd5 http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77980/2/Full%20text.pdf 906c76ca6418dd606f4acfc399bdb734 http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77980/4/Norazrizal.pdf b128730c8390cfdd29e3c02382522dc0 Universiti Malaysia Perlis (UniMAP) Transformations (Mathematics) Differential equations Integral transforms Ordinary differential Equations (ODEs) Fuzzy Sumudu transform (FST) Fuzzy numbers Institute of Engineering Mathematics
institution	Universiti Malaysia Perlis
collection	UniMAP Institutional Repository
language	English
advisor	Muhammad Zaini, Ahmad, Dr.
topic	Transformations (Mathematics) Differential equations Integral transforms Ordinary differential Equations (ODEs) Fuzzy Sumudu transform (FST) Fuzzy numbers
spellingShingle	Transformations (Mathematics) Differential equations Integral transforms Ordinary differential Equations (ODEs) Fuzzy Sumudu transform (FST) Fuzzy numbers Fuzzy Sumudu transform
description	Ordinary differential Equations (ODEs) have long been used to model real-life problems. As times goes on, researchers realized that ODEs are no longer the best modelling tool, since they are inaccurate, especially when dealing with stuff that are surrounded by uncertainties. To deal with this, researchers utilized the fuzzy set theory to propose fuzzy differential equations (FDEs). Unlike ODEs which could not cope with uncertainties at the initial values, FDEs handle this efficiently. However, the methods that can be used to deal with FDEs are very limited, and many of them are still at development stages. In this research, a new analytical method is proposed for solving a class of FDEs, including FDEs of integer order, fuzzy fractional differential equations (FFDEs), fuzzy partial differential equations (FPDEs) and system of linear fuzzy differential equations (SLFDEs). For this purpose, a novel integral transform called fuzzy Sumudu transform (FST) is proposed. This is done by integrating the fuzzy set theory and the classical Sumudu transform (CST). New properties and fundamental results concerning FST are proposed and proved mathematically. These new properties comprised results on duality with fuzzy Laplace transform (FLT), linearity, preserving, shifting, convolution, as well as theorems for fuzzy derivatives. The proposed results are then used to construct detailed procedures for solving FDEs, FFDEs, FPDEs and SLFDEs where the class of FDEs are interpreted under the strongly generalized differentiability concept. From there, the procedures are demonstrated on some examples, in order to illustrate FST applicability. Some analyses are performed where the behaviour of the solutions obtained are described in particulars. Furthermore, a comparison between the solutions obtained for the class of FDEs are compared with the solutions obtained using ODEs, where the ODEs include integer order ODEs, fractional differential equations (FrDEs), partial differential equations (PDEs) and system of linear differential equations (SLDEs). The main advantage of FST highlighted in this thesis is that it possessed the scale preserving property. This means that the transformed function, with a new domain, is a similitude to the original function. Additionally, this research provides an alternative for researchers when dealing with the class of FDEs.
format	Thesis
title	Fuzzy Sumudu transform
title_short	Fuzzy Sumudu transform
title_full	Fuzzy Sumudu transform
title_fullStr	Fuzzy Sumudu transform
title_full_unstemmed	Fuzzy Sumudu transform
title_sort	fuzzy sumudu transform
granting_institution	Universiti Malaysia Perlis (UniMAP)
granting_department	Institute of Engineering Mathematics
url	http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77980/1/Page%201-24.pdf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77980/2/Full%20text.pdf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77980/4/Norazrizal.pdf
_version_	1776104239264694272

Fuzzy Sumudu transform

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