In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.

In the present paper, the analytical solution for an exact second order fuzzy initial value problem under generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of generalized Hukuhara different...

Using the concept of Hukuhara difference, in this paper we introduce a class of new derivatives called Hukuhara delta derivative and a class of new integrals called Hukuhara delta integral for fuzzy setvalued functions on time scales. Moreover, some corresponding properties of Hukuhara delta derivative and Hukuhara delta integral are discussed. Furthermore, sufficient conditions are established...

In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville) or a solution with increasing...

In this paper, the solution to Fuzzy sequential Fractional Initial Value Problem [FFIVP] under Caputo type fuzzy fractional derivatives by a modified fractional Euler method is presented. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhara difference and strongly generalized fuzzy differentiability. The modified fractional Euler method based on a generalized Taylors formu...

Most of the existing approaches for fuzzy reliability analysis are based on fuzzy probability.  The aim of this paper is to describe fuzzy reliability using fuzzy differential equation. The reliability of a system in real world applications is affected by some uncertain parameters. Fuzzy reliability is a way to present the reliability function uncertainly using fuzzy parameters. In the proposed...

Abstract. In this paper, existence and uniqueness theorems for nonlinear fuzzy fractional Fredholm integro-differential equations are investigated. We interpret Fredholm integro-differential equations under fractional generalized Hukuhara derivatives in the Caputo sense, and for this interpretation, we prove existence results in two type of differentiability. Moreover, two examples are given to...

In the present paper, using novel generalizations of the Hukuhara di¤erence for fuzzy sets, we introduce and study new generalized di¤erentiability concepts for fuzzy valued functions. Several properties of the new concepts are investigated and they are compared to similar fuzzy di¤erentiabilities …nding connections between them. Characterization and relatively simple expressions are provided f...

In this paper, the generalized Taylor’s expansion is presented for fuzzy-valued functions. To achieve this aim, fuzzyfractional mean value theorem for integral, and some properties of Caputo generalized Hukuhara derivative are necessarythat we prove them in details. In application, the fractional Euler’s method is derived for solving fuzzy fractionaldifferential equations in the sense of Caputo...