In this article using the inverse Laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. These transfers have been expressed as the Couette flow with the fractional derivative of the Caputo sense. Also, using the Hankel contour for the Bromwich's integral, the solutions are given in terms of the generalized Airy functions.

Existence and uniqueness theorems are proved for Cauchy problems of second-order fuzzy differential equations. 1. Introduction. In 1972, Chang and Zadeh [2] first introduced the concept of fuzzy derivative, followed up ten years later by Dubois and Prade [5], who used the extension principle in their approach. In the mean time, Puri and Ralescu [12] used the notion of H-differentiability to ext...

Let K be a closed convex cone with the nonempty interior in a real Banach space and cc(K) denote the family of all nonempty convex compact subsets of K. If {F t : t ≥ 0} is a concave iteration semigroup of continuous linear set-valued functions F t : K → cc(K) with F (x) = {x} for x ∈ K, then DtF (x) = F (G(x)) for x ∈ K and t ≥ 0, where DtF (x) denotes the Hukuhara derivative of F (x) with res...

In this paper, a decomposition theorem for a (square integrable) fuzzy random variable FRV is proposed. The paper is mainly divided in two parts. In the first part, for any FRV X, we define the Hukuhara set as the family of (deterministic) fuzzy sets C for which the Hukuhara difference X ⊖H C exists almost surely; in particular, we prove that such a family is a closed (with respect to different...

This article introduces the concept of weak sharp minima for convex interval-valued functions. To solve constrained and unconstrained IOPs by WSM, we provide primal dual characterizations set WSM. The characterization is given in terms gH-directional derivatives. On other hand, to derive characterizations, propose notions support function a subset $$I({\mathbb {R}})^{n}$$ gH-subdifferentiabilit...

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

The study of set differential equations has been initiated as an independent subject and several results of interest can be found in [4–5, 10–12, 14]. The interesting feature of the set differential equations is that the results obtained in this new framework become the corresponding results of ordinary differential equations as the Hukuhara derivative and the integral used in formulating the s...