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<p>In this analysis, we conduct a comprehensive investigation into the Hyers–Ulam stability (HUS) of Volterra-type integro-differential equations formulated within the framework of time scales. Furthermore, the analysis is extended to encompass the Hyers–Ulam–Rassias stability (HURS), providing a deeper understanding of the system’s robustness under perturbations. The theoretical foundation of this work is established through the application of the fixed point alternative in complete generalized metric spaces, where contraction mapping principles are employed to guarantee the existence of solutions. To substantiate the analytical results and demonstrate their practical relevance, a representative numerical example is provided, highlighting the applicability and effectiveness of the proposed theoretical framework.</p>

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Unified Approach to Ulam Stability in Volterra Integro-Differential Equations via Time Scales

  • 期刊论文

  • 发表日期：

    2025年12月20日

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  • Kottakkaran Sooppy Nisar,
  • C. Anusha,
  • V. Vijayaraj,
  • C. Ravichandran

摘要

In this analysis, we conduct a comprehensive investigation into the Hyers–Ulam stability (HUS) of Volterra-type integro-differential equations formulated within the framework of time scales. Furthermore, the analysis is extended to encompass the Hyers–Ulam–Rassias stability (HURS), providing a deeper understanding of the system’s robustness under perturbations. The theoretical foundation of this work is established through the application of the fixed point alternative in complete generalized metric spaces, where contraction mapping principles are employed to guarantee the existence of solutions. To substantiate the analytical results and demonstrate their practical relevance, a representative numerical example is provided, highlighting the applicability and effectiveness of the proposed theoretical framework.