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<p>This paper investigates uncertain nonlinear discrete-time systems governed by Hilfer-type nabla fractional difference equations, which effectively capture memory-dependent and hereditary behaviors in discrete-time dynamics. To address epistemic uncertainty, we integrate uncertainty theory with symmetric uncertainty distributions, enabling the analysis of systems subjected to non-random but imprecise disturbances. We employ fixed-point theorems to establish the existence, uniqueness, and attractive stability of solutions. Furthermore, by developing a novel discrete Gronwall-type inequality, we derive sufficient conditions for the finite-time stability of solutions. The theoretical findings are supported by numerical examples, including applications to uncertain fractional order neural networks, demonstrating the robustness and applicability of the proposed framework in modeling and analyzing complex real-world discrete time systems.</p>

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Finite-Time Stability and Attractiveness of Uncertain Nonlinear Nabla Fractional Systems Involving Hilfer-Type Operators

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Anshul Sharma,
  • S. N. Mishra,
  • Anurag Shukla

摘要

This paper investigates uncertain nonlinear discrete-time systems governed by Hilfer-type nabla fractional difference equations, which effectively capture memory-dependent and hereditary behaviors in discrete-time dynamics. To address epistemic uncertainty, we integrate uncertainty theory with symmetric uncertainty distributions, enabling the analysis of systems subjected to non-random but imprecise disturbances. We employ fixed-point theorems to establish the existence, uniqueness, and attractive stability of solutions. Furthermore, by developing a novel discrete Gronwall-type inequality, we derive sufficient conditions for the finite-time stability of solutions. The theoretical findings are supported by numerical examples, including applications to uncertain fractional order neural networks, demonstrating the robustness and applicability of the proposed framework in modeling and analyzing complex real-world discrete time systems.