DYNAMIC EQUATIONS WITH TIME-VARYING DELAY ON TIME SCALES
DOI:
https://doi.org/10.18173/2354-1059.2026--0015Keywords:
dynamic delay equation, uniform stability, exponential stability, Lipschitz condition; Lyapunov functionAbstract
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.
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