[PDF] Top 20 Some properties of the Mittag Leffler functions and their relation with the Wright functions

... the Mittag-Leffler functions and the Wright ...The Wright function plays an important role in the solution of a linear partial differential ...The Wright function, which we denote by W(z; ... See full document

... In this paper, we presented the compositions of the fractional derivatives with the Shukla function. We obtained the reason causing the difference between the Riemann–Liouville and Caputo derivatives of the generalized ... See full document

... Atici & Eloe [6] studied linear systems of fractional nabla difference equations with constant coefficients and constructed the fundamental matrix for the homogeneous system and the causal Green’s function for the ... See full document

... The functions which are continuous but non-differentiable in integer order calculus can be characte- rized in terms of fractional calculus and especially through Holder exponent [10] ...differentiable ... See full document

... First, expressing the generalized multiple-index Mittag-Leffler function in serie with the help of equation (2.1), the I-function of r variables in series with the help of equation (1.4), the general class ... See full document

... of some integral formulae involving generalized Galu e′ type Struve function in terms of Fox-Wright ...with some known special functions such as Struve function, Mittag-Leffler ... See full document

... Kiryakova, Multiple (multiondex) Mittag-Leffler functions and relations to generalized frac- tional calculus, Journal of Computational and Applied Mathematics , 118(2000), 241-259. [11] [r] ... See full document

... extended Mittag-Leffler function based on the well known Lavoie and Trot- tier integral formula and the obtain results are express in term of extended Wright-type ... See full document

... convex functions, which is called the class of exponential convex functions, was introduced and studied by Antczak [63] and Dragomir et ...mathematical properties along with their potential ap- ... See full document

... extended Mittag-Leffler functions by using the extended Beta functions (Chaudhry et ...obtain some integral representations of ...these functions is given in terms of generalized ... See full document

... of Mittag-Leffler function ; its various properties including differentiation,Laplace ,Beta, and Mellin transforms,and generalized hypergeometric series form and its relationship with other type of ... See full document

... In this paper, using the principal of differential subordination, we obtain some properties of certain class of p -valent meromorphic functions, which are defined by Mittag-Leffler funct[r] ... See full document

... The analogous theory for nabla discrete fractional calculus was initiated by Miller & Ross [21], Gray & Zhang [10] and Atici & Eloe [6], where basic approaches, definitions, and properties of ... See full document

... In this paper, we study pre-starlikeness and deduce the convexity and starlikeness of order 1/2. We also investigate the starlikeness of order 2μ + η – 1. Furthermore, we find the convexity of Mittag-Leffler ... See full document

... First, expressing the generalized multiple-index Mittag-Leffler function in serie with the help of equation (2.1), the Aleph-function of r variables in series with the help of equation (1.6), the general ... See full document

... multiple-index Mittag-Leffler function, the hyperbolic functions, the multivariable Aleph-function, a class of polynomials of several variables a sequence of functions and the multivariable ... See full document

... Some integral transforms of the generalized k-Mittag-Leffler function are established and the results are expressed in terms of the generalized Wright function. By taking δ = 1 and using the ... See full document

... generalized Mittag-Leffler function operator introduced by Shukla and Prajapati ...paper. Some special cases of the established results are also deduced as ...the Mittag-Leffler function occurs ... See full document

... In this paper we establish some inequalities of Hadamard’s type involving Godunova-Levin functions, P-functions, quasi-convex functions, J- quasi-convex functions, Wright-convex function[r] ... See full document

... Γ − and this corresponds to a fading memory since the kernel decays with time. Thus a fractional derivative incorporates a fading memory although the remnants of the memory lingers on for ever with decreasing intensity ... See full document