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
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
Idioma: inglés
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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.