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Linearized asymptotic stability for nabla Riemann-Liouville fractional difference equation

Anh Pham The, Czornik Adam, Niezabitowski Michał

Archives of Control Sciences

2024

Vol. 34, No. 3

569--588

In this paper, we present a theorem about stability of nonlinear fractional difference equation with Riemann-Liouvile difference operator. The result is a version of classical theorem on linear approximation and to derive them, we prove the variation of constants formula for nabla Riemann-Liouville fractional difference equations. We also present some results concerning the existence and uniqueness of the equation under consideration.