Numerical computation of exponential functions in frame of Nabla fractional calculus

Exponential functions play an essential role in describing the qualitative properties of solutions of nabla fractional difference equations. In this article, we illustrate their asymptotic behavior. We know that these functions involve infinite series of ratios of gamma functions, and it is challenging to compute them. For this purpose, we propose a novel matrix technique to compute the addressed functions numerically. The results are supported by illustrative examples. The proposed method can be extended to obtain numerical solutions for non-homogeneous nabla fractional difference equations.