Abstract
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.
Highlights
The applications of differential equations in science and engineering problems are well known
The applicability of difference equations is gaining an important role in computer science, control theory, image processing, digital filter design, numerical analysis, and finite element techniques
Fractional differential equations have been applied in many areas of science and engineering
Summary
The applications of differential equations in science and engineering problems are well known. In [19], the authors presented basic qualitative and quantitative results for solutions to nonlinear dynamic equations on time scales with applications to economic modeling.
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