Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability

Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability

We study in this paper the Atangana-Baleanu fractional derivative of fuzzy functions based on the generalized Hukuhara difference. Under the condition of gH-Atangana-Baleanu fractional differentiability, we prove the generalized necessary and sufficient optimality conditions for problems of the fuzz...

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Main Authors: Jianke Zhang, Gaofeng Wang, Xiaobin Zhi, Chang Zhou
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2018/2740678
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spelling doaj-17094e12689b43618b521ee3eac19fd82020-11-24T22:48:57ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/27406782740678Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu DifferentiabilityJianke Zhang0Gaofeng Wang1Xiaobin Zhi2Chang Zhou3Department of Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, ChinaDepartment of Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, ChinaDepartment of Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, ChinaDepartment of Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, ChinaWe study in this paper the Atangana-Baleanu fractional derivative of fuzzy functions based on the generalized Hukuhara difference. Under the condition of gH-Atangana-Baleanu fractional differentiability, we prove the generalized necessary and sufficient optimality conditions for problems of the fuzzy fractional calculus of variations with a Lagrange function. The new kernel of gH-Atangana-Baleanu fractional derivative has no singularity and no locality, which was not precisely illustrated in the previous definitions.http://dx.doi.org/10.1155/2018/2740678
collection DOAJ
language English
format Article
sources DOAJ
author Jianke Zhang
Gaofeng Wang
Xiaobin Zhi
Chang Zhou
spellingShingle Jianke Zhang
Gaofeng Wang
Xiaobin Zhi
Chang Zhou
Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability
Journal of Function Spaces
author_facet Jianke Zhang
Gaofeng Wang
Xiaobin Zhi
Chang Zhou
author_sort Jianke Zhang
title Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability
title_short Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability
title_full Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability
title_fullStr Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability
title_full_unstemmed Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability
title_sort generalized euler-lagrange equations for fuzzy fractional variational problems under gh-atangana-baleanu differentiability
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2018-01-01
description We study in this paper the Atangana-Baleanu fractional derivative of fuzzy functions based on the generalized Hukuhara difference. Under the condition of gH-Atangana-Baleanu fractional differentiability, we prove the generalized necessary and sufficient optimality conditions for problems of the fuzzy fractional calculus of variations with a Lagrange function. The new kernel of gH-Atangana-Baleanu fractional derivative has no singularity and no locality, which was not precisely illustrated in the previous definitions.
url http://dx.doi.org/10.1155/2018/2740678
work_keys_str_mv AT jiankezhang generalizedeulerlagrangeequationsforfuzzyfractionalvariationalproblemsunderghatanganabaleanudifferentiability
AT gaofengwang generalizedeulerlagrangeequationsforfuzzyfractionalvariationalproblemsunderghatanganabaleanudifferentiability
AT xiaobinzhi generalizedeulerlagrangeequationsforfuzzyfractionalvariationalproblemsunderghatanganabaleanudifferentiability
AT changzhou generalizedeulerlagrangeequationsforfuzzyfractionalvariationalproblemsunderghatanganabaleanudifferentiability
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