Related papers: Computation of the Wright function from its integr…
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 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…
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…
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…
In the framework of higher transcendental functions the Wright functions of the second kind have increased their relevance resulting from their applications in probability theory and, in particular, in fractional diffusion processes. Here,…
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 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 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…
The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-) periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation…
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…
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.
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
We describe a method for calculating the roots of special functions satisfying second order linear ordinary differential equations. It exploits the recent observation that the solutions of a large class of such equations can be represented…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approximation is now a routine technology, this provides an easy new…
In this paper, we will discuss several radii problems related to Wright Function involving four parameters.
This paper introduces a new numerical method for approximating the Lambert W function in the real domain. The method transforms the function into a simpler form that allows iterative refinement of an initial guess. Two iterative strategies…
This short note presents the Lambert W(x) function and its possible application in the framework of physics related to the Pierre Auger Observatory. The actual numerical implementation in C++ consists of Halley's and Fritsch's iteration…
The Lambert W(x) function and its possible applications in physics are presented. The actual numerical implementation in C++ consists of Halley's and Fritsch's iterations with initial approximations based on branch-point expansion,…