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_-1u)(t) = λ u(t - 1), t N_1, where 0 < u < 1, λ R, abla^ u_-1u denotes the u-th Riemann–Liouville nabla fractional difference of u based at -1, and 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.