Mittag–Leffler Functions in Discrete Time

Abstract

In this paper, we give an efficient way to calculate the values of the Mittag–Leffler (h-ML) function defined in discrete time hN, where h>0 is a real number. We construct a matrix equation that represents an iteration scheme obtained from a fractional h-difference equation with an initial condition. Fractional h-discrete operators are defined according to the Nabla operator and the Riemann–Liouville definition. Some figures and examples are given to illustrate this new calculation technique for the h-ML function in discrete time. The h-ML function with a square matrix variable in a square matrix form is also given after proving the Putzer algorithm.