The main aim of this paper is to establish two generalized integral formulas involving the extended Mittag-Leffler function based on the well known Lavoie and Trottier integral formula and the obtain results are express in term of extended Wright-type function. Also, we establish certain special cases of our main result.

Abstract. The object of the present paper is to establish an integral formula involving Wright generalized Bessel function (or generalized Bessel-Maitland function) J ν,q (z) defined by Singh et al. [21], which is expressed in the terms of generalized (Wright) hypergeometric functions. Some interesting special cases involving Bessel functions, generalized Bessel functions, generalized Mittag-Le...

We study the first passage time (FPT) problem for biased continuous time random walks. Using the recently formulated framework of fractional Fokker-Planck equations, we obtain the Laplace transform of the FPT density function when the bias is constant. When the bias depends linearly on the position, the full FPT density function is derived in terms of Hermite polynomials and generalized Mittag-...

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Lévy alpha -stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler...

In this paper a closed form solution of a fractional integro-differential equation of Volterra type involving Mittag-Leffler function has been obtained using straight forward technique of Sumudu transform. Some particular cases have also been considered.

In this paper, the solution of a class of fractional Kinetic equation involving generalized I-function has been discussed. Special cases involving the Ifunction, H-function, generalized M-series, generalized Mittag-Leffler functions are also discussed. Results obtained are related to recent investigations of possible astrophysical solutions of the solar neutrino problem.

UNLABELLED This paper deals with the study of a generalized function of Mittag-Leffler type. Various properties including usual differentiation and integration, Euler(Beta) transforms, Laplace transforms, Whittaker transforms, generalized hypergeometric series form with their several special cases are obtained and relationship with Wright hypergeometric function and Laguerre polynomials is also...

In this paper a new function called as K-function, which is an extension of the generalization of the Mittag-Leffler function[10,11] and its generalized form introduced by Prabhakar[20], is introduced and studied by the author in terms of some special functions and derived the relations that exists between the Kfunction and the operators of Riemann-Liouville fractional integrals and derivatives.