Asymptotic Stability of a Linear Nabla Fractional Difference Equation - Jonnalagadda, Jagan Mohan (Discontinuity, Nonlinearity, and Complexity, 2026)
In this work, we consider the two-term linear nabla fractional difference equation $$ {(} abla^{ u}_{-1}u{)}(t) = λ u(t - 1), \quad t \in \mathbb{N}_{1}, $$ where $0 < u < 1$, $λ \in \mathbb{R}$, $ abla^{ u}_{-1}u$ denotes the $ u$-th Riemann--Liouville nabla fractional difference of $u$ based at $-1$, and $\mathbb{N}_{1} = \{1, 2, 3, …\}$. First we transform this nabla fractional difference equation into a Volterra difference equation of convolution-type. Using the well established qualitative theory of Volterra difference equations, we obtain sufficient conditions on asymptotic stability of solutions of the nabla fractional difference equation.