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Discontinuity, Nonlinearity, and Complexity 12(3) (2023) 575--581 | DOI:10.5890/DNC.2023.09.007

Jagan Mohan Jonnalagadda

Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad - 500078, Telangana, India

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Abstract

In this work, we consider the two-term linear nabla fractional difference equation \begin{equation*} \label{FDE L} {(}\nabla^{\nu}_{-1}u{)}(t) = \lambda u(t - 1), \quad t \in \mathbb{N}_{1}, \end{equation*} where $0 < \nu < 1$, $\lambda \in \mathbb{R}$, $\nabla^{\nu}_{-1}u$ denotes the $\nu$-th Riemann--Liouville nabla fractional difference of $u$ based at $-1$, and $\mathbb{N}_{1} = \{1, 2, 3, \cdots\}$. 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.

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