Abstract. This paper deals with the solution of unified fractional reactiondiffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. On account of the most general character of the derived results, numerous results on fractional reaction, fractional diffusi...

Abstract In a recent paper, Saxena et al.[1] developed the solutions of three generalized fractional kinetic equations in terms of the Mittag-Leffler functions. The object of the present paper is to further derive the solution of further generalized fractional kinetic equations. The results are obtained in a compact form in terms of generalized Mittag-Leffler functions. Their relation to fundam...

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.

The problem of calculating the Mittag-Leffler function Eρ,μ(z) is considered in paper. To solve this integral representations for are transformed such a way that they could not contain complex variables and parameters. Integral written form allow one to use standard methods numerical integration calculate integrals contained them. verify correctness obtained was calculated both with formulas kn...

Generalization of the integral representation gamma function has been obtained, which shows that Hankel contour assumes rotation in complex plane. The range admissible values for angle is set. Using this representation, generalization Mittag-Leffler obtained expresses value terms integral.

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-...