相关论文: The Prabhakar or three parameter Mittag--Leffler f…

We employ Mittag-Leffler type kernels to solve a system of fractional differential equations using fractal-fractional (FF) operators with two fractal and fractional orders. Using the notion of FF-derivatives with nonsingular and nonlocal…

In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local…

The two-dimensional multifractal detrended fluctuation analysis is applied to reveal the multifractal properties of the fracture surfaces of foamed polypropylene/polyethylene blends at different temperatures. Nice power-law scaling…

Experimental data collected to provide us with information on the course of dielectric relaxation phenomena are got according to two distinct schemes: one can measure either the time decay of depolarization current or use methods of the…

In this work, the first initial-boundary value problem for a sub-diffusion equation involving the regularized Prabhakar fractional derivative is studied. The problem is solved by reducing it to two initial-boundary value problems using the…

We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…

We give a functorial characterization of Mittag-Leffler modules and strict Mittag-Leffler modules.

We propose a procedure for estimating the parameters of the Mittag-Leffler (ML) and the generalized Mittag-Leffler (GML) distributions. The algorithm is less restrictive, computationally simple, and necessary to make these models usable in…

In this article, we focus on the construction of multivariate fractal functions in Lebesgue spaces along with some properties of associated fractal operator. First, we give a detailed construction of the fractal functions belonging to…

The solutions of traditional fractional differential equations neither satisfy group property nor generate dynamical systems, so the study on hyperbolicity is in blank. Relying on the new proposed conformable fractional derivative, we…

We calculate some infinite sums containing the digamma function in closed-form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as…

This paper is devoted to the general theory of systems of time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order…

In this paper we consider suitable families of power series distributed random variables, and we study their asymptotic behavior in the fashion of large (and moderate) deviations. We also present two examples of fractional counting…

Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…

In this paper, we introduce a delayed Mittag-Leffler type function. With the help of the delayed Mittag-Leffler type functions, we give an explicit formula of solutions to linear nonhomogeneous fractional time-delay Langevin equations…

Density functional perturbation theory is a well-established method to study responses of molecules and solids, especially responses to atomic displacements or to different perturbing fields (electric, magnetic). Like for density functional…

Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such…

Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…

In reaction rate theory, in input-output type models and in reaction-diffusion problems when the total derivatives are replaced by fractional derivatives the solutions are obtained in terms of Mittag-Leffler functions and their…

Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…