Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary In the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion equation of distributed order is formulated and discussed. In these equations, the time-fractional derivative is defined in the Caputo sense. In contrast to the Riemann...

In this paper, we study a new operational numerical method for hybrid fuzzy fractional differential equations by using of the hybrid functions under generalized Caputo- type fuzzy fractional derivative. Solving two examples of hybrid fuzzy fractional differential equations illustrate the method.

This paper is devoted to the study of gH-Clarke derivative for interval-valued functions. To find properties derivative, concepts limit superior, inferior, and sublinear functions are studied in sequel. It proved that upper a gH-Lipschitz continuous function (IVF) always exists. For convex IVF, found be identical with gH-directional derivative. observed IVF. Several numerical examples provided ...

In this paper, we further discuss the properties of three kinds of fractional derivatives: the Grünwald–Letnikov derivative, the Riemann–Liouville derivative and the Caputo derivative. Especially, we compare the Riemann–Liouville derivative with the Caputo derivative. And sequential property of the Caputo derivative is also derived, which is helpful in translating the higher fractional-order di...

In this paper we study a fuzzy predator-prey model with functional response arctan(ax). The derivatives are approximated using the generalized Hukuhara derivative. To execute numerical simulation, use Runge-Kutta method. results obtained over time for evolution and population presented numerically graphically some conclusions.

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...

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...

In this paper, images of the tempered Ψ-Hilfer fractional integral and Ψ-Caputo derivative under generalized Laplace transform are derived. The results applied to find a solution an initial value problem for nonhomogeneous linear differential equation with order α n− 1 <α<n N. An illustrative example is given 0 <α<1 comparing solutions same but different tempering Ψ.