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<p>This paper investigates the stability analysis of Hilfer-like fractional difference equations using Grönwall’s inequality. We consider an initial value problem associated with the discrete fractional nabla operator, extending classical difference equations to a broader fractional framework. By leveraging Grönwall’s inequality in the discrete fractional setting, we establish fundamental stability criteria, including Ulam-Hyers and Ulam-Hyers-Rassias stability.</p>

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Ulam-Hyers Stability for Hilfer-Like Nabla Fractional Difference Equations Using Grönwall’s Inequality

  • 期刊论文

  • 发表日期：

    2025年9月26日

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

摘要

This paper investigates the stability analysis of Hilfer-like fractional difference equations using Grönwall’s inequality. We consider an initial value problem associated with the discrete fractional nabla operator, extending classical difference equations to a broader fractional framework. By leveraging Grönwall’s inequality in the discrete fractional setting, we establish fundamental stability criteria, including Ulam-Hyers and Ulam-Hyers-Rassias stability.