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Analysis of Nonlinear Impulsive Adjoint Integro-Dynamic Equations on Time Scale

  • Syed Omar Shah [1] ; Sanket Tikare [4] ; Rizwan Rizwan [2] ; Usman Riaz [3]
    1. [1] Zhejiang Normal University

      Zhejiang Normal University

      China

    2. [2] Renmin University of China

      Renmin University of China

      China

    3. [3] Qurtuba University of Science and Information Technology

      Qurtuba University of Science and Information Technology

      Pakistán

    4. [4] Ramniranjan Jhunjhunwala College
    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
  • Idioma: inglés
  • Enlaces
  • Resumen

    • This article is devoted to the investigation of the existence and uniqueness of solutions and Ulam-type stability of nonlinear impulsive Hammerstein integro-dynamic, nonlinear impulsive mixed integro-dynamic, and nonlinear impulsive Volterra Fredholm Hammerstein integro-dynamic adjoint equations on finite time scale intervals. Primary tools utilized to verify the existence and uniqueness of solutions for the discussed models are the Banach contraction principle and the Picard operator. Furthermore, Ulam-type stabilities are obtained by an extended integral impulsive inequality on time scales. To address the challenges in achieving the desired outcomes, certain assumptions are introduced. To demonstrate the practical applications of the obtained results, illustrative examples are presented.

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