Using the Bernstein theorem we give a simple proof of complete monotonicity three parameter generalized Mittag-Leffler function $E_{\alpha, \beta}^{\gamma}(-x)$ for $x \geq 0$ and suitably adjusted parameters $\alpha$, $\beta$ $\gamma$

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...

In this paper a new generalization of the hyper-Poisson distribution is proposed using the Mittag-Leffler function. The hyper-Poisson, displaced Poisson, Poisson and geometric distributions among others are seen as particular cases. This Mittag-Leffler function distribution (MLFD) belongs to the generalized hypergeometric and generalized power series families and also arises as weighted Poisson...

A remarkably large number of unified integrals involving the Mittag–Leffler function have been presented. Here, with same technique as Choi and Agarwal, we propose establishment two generalized integral formulas a multivariate function, which are expressed in terms Lauricella series due to Srivastava Daoust. We also present some interesting special cases.