In this paper, we study the existence criteria for Ψ-bounded solutions of Sylvester matrix dynamical systems on time scales. The advantage of studying this system is it unifies continuous and discrete systems. First, we prove a necessary and sufficient condition for the existence of atleast one Ψ-bounded solution for Sylvester matrix dynamical systems on time scales, for every Lebesgue Ψdeltaintegrable function F, on time scale T +. Further, we obtain a result relating to asymptotic behavior of Ψ-bounded solutions of this equation. The results are illustrated with suitable examples.
In this paper, we have constructed a sequence of soft points in one soft set with respect to a fixed soft point of another soft set. The convergence and boundedness of these sequences in soft ∆-metric spaces are defined and their properties are established. Further, the complete soft ∆-metric spaces are introduced by defining soft ∆-Cauchy sequences.
In this paper, we establish sufficient conditions for various stability aspects of a nonlinear Volterra integro-dynamic matrix Sylvester system on time scales. We convert the nonlinear Volterra integro-dynamic matrix Sylvester system on time scale to an equivalent nonlinear Volterra integro-dynamic system on time scale using vectorization operator. Sufficient conditions are obtained to this system for stability, asymptotic stability, exponential stability, and strong stability. The obtained results include various stability aspects of the matrix Sylvester systems in continuous and discrete models.
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