In this paper we introduce a new multiple-parameters (multi-index) extension of the Wright function that arises from an eigenvalue problem for case hyper-Bessel operator involving Caputo fractional derivatives. We show by giving particular values to parameters involved in special function, leads some known functions (as classical α-Mittag-Leffler Tricomi etc.) on their turn appear as cases so-c...

In this paper, we use the Mittag-Leffler addition formula to solve Green function of generalized time fractional diffusion equation in whole plane and prove convergence function.

We introduce and study a new function called R-function, which is an extension of the generalized Mittag-Leffler function. We derive the relations that exist between the R-function and Saigo fractional calculus operators. Some results derived by Samko et al. (1993), Kilbas (2005), Kilbas and Saigo (1995), and Sharma and Jain (2009) are special cases of the main results derived in this paper.

Let C be a category with strong monomorphic strong coimages, that is, every morphism ƒ of C factors as ƒ = u ° g so that g is a strong epimorphism and u is a strong monomorphism and this factorization is universal. We define the notion of strong Mittag-Leffler property in pro-C. We show that if ƒ : X → Y is a level morphism in pro-C such that ( ) p Y ! " is a strong epimorphism for all β > α, t...

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 In this paper, we employ the generalized fractional calculus operators on the generalized Mittag-Leffler function. Some results associated with generalized Wright function are obtained. Recent results of Chaurasia and Pandey are obtained as special cases. 2000 MATHEMATICS SUBJECT CLASSIFICATION 33C45, 47G20, 26A33.

*Correspondence: [email protected] 3Department of Mathematical Sciences, UAE University, Al Ain, United Arab Emirates Full list of author information is available at the end of the article Abstract In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involvin...