Fractional calculus of linear correlated fuzzy-valued functions related to Frechet differentiability

In this paper, we will introduce some types of Frechet fractional derivative defined on the class of linear correlated fuzzy valued functions. Firstly, we study Frechet derivative and R-derivative of integer order and investigate their relationship with the well-known generalized Hukuhara derivatives in fuzzy metric space. Secondly, the Riemann-Liouville fractional integral of linear correlated fuzzy-valued functions is well-defined via an isomorphism between R-2 and subspace of fuzzy numbers space RF. That allows us to introduce three types of Frechet fractional derivatives, which are Frechet Caputo derivative, Frechet RiemannLiouville derivative and Frechet Caputo-Fabrizio derivative. Moreover, some common properties of fuzzy Laplace transform for linear correlated fuzzy-valued function are investigated. Finally, some applications to fuzzy fractional differential equations are presented to demonstrate the usefulness of theoretical results. (C) 2020 Elsevier B.V. All rights reserved.