On explicit stability conditions for a linear fractional difference system

Abstract

Abstract The paper describes the stability area for the difference system (Δαy)(n + 1 − α) = Ay(n), n= 0, 1, . . . , with the Caputo forward difference operator Δα of a real order α ∈ (0, 1) and a real constant matrix A. Contrary to the existing result on this topic, our stability conditions are fully explicit and involve the decay rate of the solutions. Some comparisons with a difference system of the Riemann- Liouville type are discussed as well, including related consequences and illustrating examples.