Related papers: Wright functions of the second kind and Whittaker …
In this review paper we stress the importance of the higher transcendental Wright functions of the second kind in the framework of Mathematical Physics.We first start with the analytical properties of the classical Wright functions of which…
In this tutorial survey we recall the basic properties of the special function of the Mittag-Leffler and Wright type that are known to be relevant in processes dealt with the fractional calculus. We outline the major applications of these…
In the present review we survey the properties of a transcendental function of the Wright type, nowadays known as M-Wright function, entering as a probability density in a relevant class of self-similar stochastic processes that we…
In this survey paper we consider some applications of the Wright function with special emphasis of its key role in the partial differential equations of fractional order. It was found that the Green function of the time-fractional…
We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular…
The Wright function arises in the theory of the fractional differential equations. It is a very general mathematical object having diverse connections with other special and elementary functions. The Wright function provides a unified…
In this note we prove some new results about the application of Wright functions of the first kind to solve fractional differential equations with variable coefficients. Then, we consider some applications of these results in order to…
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…
In this survey we discuss derivatives of the Wright functions (of the first and the second kind) with respect to parameters. Differentiation of these functions leads to infinite power series with coefficient being quotients of the digamma…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
The fractional Poisson process and the Wright process (as discretization of the stable subordinator) along with their diffusion limits play eminent roles in theory and simulation of fractional diffusion processes. Here we have analyzed…
In this paper we find the partial sums of two kinds normalized Wright functions and the partial sums of Alexander transform of these normalized Wright functions.
In this work, a new relationship is established between the solutions of higher fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As…
The classes of n-Wright-convex functions and n-Jensen-convex functions are compared with each other. It is shown that for any odd natural number $n$ the first one is the proper subclass of the second one. To reach this aim new tools…
In this paper, we introduce a new multiple-parameters (multi-index) extension of the Wright function that arises from an eigenvalue problem for a case of hyper-Bessel operator involving Caputo fractional derivatives. We show that by giving…
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…
The Mittag-Leffler function plays a role of central importance in the theory of fractional derivatives. In this brief note we discuss the properties of this function and its connection with the Wright-Bessel functions and with a new family…
Quark distribution and spectator functions are estimated in a diquark spectator model. The representation of the functions in terms of non-local operators together with the rather simple model allow estimates for the yet experimentally…
This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have been discussed in the first part. Pricing…
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…