Stability and solutions of adjoint nonlinear impulsive neutral mixed integral equations in dynamic systems

This research explores the existence, uniqueness, and Ulam-type stability of solutions for nonlinear impulsive neutral Hammerstein mixed integral dynamic equations over finite time scale intervals. The research establishes precise conditions ensuring the existence and uniqueness of solutions, utilizing the principles of Banach’s contraction theorem along with the Picard iterative operator. By adapting integral impulsive inequalities to the time scale framework, Ulam-type stability is examined, providing a unified and generalized approach. Carefully crafted assumptions offer a solid theoretical foundation for addressing the complexities of these equations. The practical significance of the findings is illustrated through a detailed example, emphasizing their versatility and applicability in dynamic system analysis and real-world problem-solving.