Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n-1<β<n

The main aim in this paper is to use all the possible arrangements of objects such that r1 of them are equal to 1 and r2 (the others) of them are equal to 2, in order to generalize the definitions of Riemann-Liouville and Caputo fractional derivatives (about order 0<β<n) for a fuzzy-valued fun...

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Main Authors:	Amal Khalaf Haydar, Ruaa Hameed Hassan
Format:	Article
Language:	English
Published:	Hindawi Limited 2016-01-01
Series:	Mathematical Problems in Engineering
Online Access:	http://dx.doi.org/10.1155/2016/6380978

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spelling	doaj-7dc74a5e06be4b288e6c3d9cc97ab7272020-11-24T22:25:59ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472016-01-01201610.1155/2016/63809786380978Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n-1<β<nAmal Khalaf Haydar0Ruaa Hameed Hassan1Department of Mathematics, Faculty of Education for Girls, Kufa University, Najaf, IraqDepartment of Mathematics, Faculty of Education for Girls, Kufa University, Najaf, IraqThe main aim in this paper is to use all the possible arrangements of objects such that r1 of them are equal to 1 and r2 (the others) of them are equal to 2, in order to generalize the definitions of Riemann-Liouville and Caputo fractional derivatives (about order 0<β<n) for a fuzzy-valued function. Also, we find fuzzy Laplace transforms for Riemann-Liouville and Caputo fractional derivatives about the general fractional order n-1<β<n under H-differentiability. Some fuzzy fractional initial value problems (FFIVPs) are solved using the above two generalizations.http://dx.doi.org/10.1155/2016/6380978
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Amal Khalaf Haydar Ruaa Hameed Hassan
spellingShingle	Amal Khalaf Haydar Ruaa Hameed Hassan Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n-1<β<n Mathematical Problems in Engineering
author_facet	Amal Khalaf Haydar Ruaa Hameed Hassan
author_sort	Amal Khalaf Haydar
title	Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n-1<β<n
title_short	Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n-1<β<n
title_full	Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n-1<β<n
title_fullStr	Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n-1<β<n
title_full_unstemmed	Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n-1<β<n
title_sort	generalization of fuzzy laplace transforms of fuzzy fractional derivatives about the general fractional order n-1<β<n
publisher	Hindawi Limited
series	Mathematical Problems in Engineering
issn	1024-123X 1563-5147
publishDate	2016-01-01
description	The main aim in this paper is to use all the possible arrangements of objects such that r1 of them are equal to 1 and r2 (the others) of them are equal to 2, in order to generalize the definitions of Riemann-Liouville and Caputo fractional derivatives (about order 0<β<n) for a fuzzy-valued function. Also, we find fuzzy Laplace transforms for Riemann-Liouville and Caputo fractional derivatives about the general fractional order n-1<β<n under H-differentiability. Some fuzzy fractional initial value problems (FFIVPs) are solved using the above two generalizations.
url	http://dx.doi.org/10.1155/2016/6380978
work_keys_str_mv	AT amalkhalafhaydar generalizationoffuzzylaplacetransformsoffuzzyfractionalderivativesaboutthegeneralfractionalordern1bn AT ruaahameedhassan generalizationoffuzzylaplacetransformsoffuzzyfractionalderivativesaboutthegeneralfractionalordern1bn
_version_	1725755264404029440

Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n-1<β<n

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