On a recurrence relation of generalized Mittag-Leffler function.
On asymptotics of discrete Mittag-Leffler function
The (modified) two-parametric Mittag-Leffler function plays an essential role in solving the so-called fractional differential equations. Its asymptotics is known (at least for a subset of its domain and special choices of the parameters). The aim of the paper is to introduce a discrete analogue of this function as a solution of a certain two-term linear fractional difference equation (involving both the Riemann-Liouville as well as the Caputo fractional -difference operators) and describe its...
On Fractional Helmholtz Equations
MSC 2010: 26A33, 33E12, 33C60, 35R11In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.
On generalisation of polynomials in complex plane.
On q–Analogues of Caputo Derivative and Mittag–Leffler Function
Mathematics Subject Classification: 33D60, 33E12, 26A33Based on the fractional q–integral with the parametric lower limit of integration, we consider the fractional q–derivative of Caputo type. Especially, its applications to q-exponential functions allow us to introduce q–analogues of the Mittag–Leffler function. Vice versa, those functions can be used for defining generalized operators in fractional q–calculus.