Time-domain response of nabla discrete fractional order systems

TL;DR

This paper analyzes the time-domain response of nabla discrete fractional order systems, establishing fundamental properties and demonstrating their behavior through theoretical analysis and a numerical example.

Contribution

It introduces new theoretical results on existence, uniqueness, and dynamic behavior of nabla discrete fractional systems, supported by a numerical validation.

Findings

Existence and uniqueness of system response established

Dynamic behavior of zero input response characterized

Numerical example confirms theoretical results

Abstract

This paper investigates the time--domain response of nabla discrete fractional order systems by exploring several useful properties of the nabla discrete Laplace transform and the discrete Mittag--Leffler function. In particular, we establish two fundamental properties of a nabla discrete fractional order system with nonzero initial instant: i) the existence and uniqueness of the system time--domain response; and ii) the dynamic behavior of the zero input response. Finally, one numerical example is provided to show the validity of the theoretical results.