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Journal of Function Spaces
Volume 2018 (2018), Article ID 2740678, 15 pages
https://doi.org/10.1155/2018/2740678
Research Article

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

Department of Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, China

Correspondence should be addressed to Jianke Zhang; moc.361@hzeknaij

Received 14 September 2017; Accepted 1 January 2018; Published 19 March 2018

Academic Editor: Talat Nazir

Copyright © 2018 Jianke Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.