The aim of this paper is to use the concept of the generalized H-derivative to deﬁne fuzzy Caputo’s H-derivative of order β ∈(1,2]. Our deﬁnition is an extension of fuzzy Caputo’s H-derivative of order β ∈(0,1] and higher order H-derivative of integerorder. After that, we study fuzzy fractional initial value p roblems of order β ∈(1,2] and give an algorithm to solve them based onthe characterization theorem. Finally, we apply the reprod ucing kernel Hilbert space method to obtain approximate solutions of second order fuzzy fractional initial value problems and give some numerical examples.
Digital Object Identifier (DOI)
Hasan, Shatha; Alawneh, Ahmad; Al-Momani, Mohammad; and Momani, Shaher
"Second Order Fuzzy Fractional Differential Equations Under Caputo’s H-Differentiability,"
Applied Mathematics & Information Sciences: Vol. 11
, Article 6.
Available at: https://dc.naturalspublishing.com/amis/vol11/iss6/6