Mittag–Leffler Functions in Discrete Time

Fractal and Fractional

article

Ferhan M. Atıcı¹  Samuel Chang²  Jagan Mohan Jonnalagadda³ 

[1] Department of Mathematics, Western Kentucky University;Booth School of Business, University of Chicago;Department of Mathematics, Birla Institute of Technology and Science Pilani

关键词: discrete Mittag–Leffler function;    matrix Mittag–Leffler function;    nabla operator;    fractional h-discrete calculus;   

DOI  :  10.3390/fractalfract7030254

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

In this paper, we give an efficient way to calculate the values of the Mittag–Leffler (h-ML) function defined in discrete time h N, where h0 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.

【 授权许可】

CC BY