DYNAMIC EQUATIONS WITH TIME-VARYING DELAY ON TIME SCALES - Thu Ha, Nguyen (HNUE Journal of Science: Journal of Natural Sciences, 2026)
This paper investigates dynamic delay equations on time scales. Due to the lack of a well-defined subtraction, the formulation of delay equations in this setting is nontrivial. We first introduce a suitable representation of delay dynamic equations on time scales. We then prove the existence and uniqueness of solutions, as well as the uniform exponential stability for Δ-dynamic delay equations via Lyapunov direct method. The obtained results extend existing works and provide verifiable conditions in the framework of time scale calculus.