Asymptotic stability of linear tempered fractional difference system

Abstract Tempered fractional difference system, as a kinetic evolution on time scales that incorporates a tempered characteristic factor within the framework of the fractional difference equation, exhibits considerable potential in elucidating specific physical phenomena. However, essential traits such as its asymptotic stability remain unclear. In view of this, the primary intention of this paper is to determine the exact regions of asymptotic stability and instability for the linear tempered fractional difference system with the aid of the discrete Laplace transform technique. Not only that, a joint analysis is devoted to clarifying the dependence of the asymptotically stable regions with respect to the key parameters, specifically the fractional order and the tempered characteristic factor . Notably, in contrast to the classical inverse power law over time scales, a more generalized compound decay law incorporating the tempered characteristic factor is also found. Besides, two examples are also provided to examine the validity of the main results.