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Existence and Stability Analysis of Implicit Neutral Switched Volterra Fredholm Hammerstein Impulsive Integro-Delay Dynamic System

  • Akbar Zada [1] ; Muhammad Abbas [1] ; Afef Kallekh [2]
    1. [1] University of Peshawar

      University of Peshawar

      Pakistán

    2. [2] King Khalid University

      King Khalid University

      Arabia Saudí

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 1, 2026
  • Idioma: inglés
  • Enlaces
  • Resumen

    • This article presents a pioneering study of implicit impulsive switched VolterraFredholm-Hammerstein integro-delay dynamic system on arbitrary time scales, providing a unified framework for modeling complex phenomena in continuous, discrete, and hybrid time domains. By using time scale theory, operator algebra, and Banach fixed point theory, we establish the existence and uniqueness of solution and analyze Ulam-type stability results. The Volterra-Fredholm-Hammerstein structure allows for the incorporation of memory effects, nonlinear interactions, and non-local influences, making it an ideal framework for modeling real-world systems. Our findings have significant implications for systems exhibiting impulsive behavior, such as population dynamics, disease pattern analysis, and control systems. The results can be applied to optimize system performance, predict behavior, and inform decisionmaking in various fields. A theoretical and simulated example is given to demonstrate the efficacy and practical relevance of our approach, highlighting its potential to tackle complex problems in a wide range of applications.

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