Repeated we take care, since in general evaluate without assumptions. ![]() But if some of the eigenvalues of the coefficient matrix are If all the eigenvalues of the coefficient matrix are real and distinct, then we can construct a solution of the system without any difficulty. ![]() In this paper, for the development of theory, we construct the fundamental matrices for the system of linear differential equations on time scales. It provides a new direction of research in dynamical process with time scales. For the time scale calculus and notation for delta differentiation, as well as concepts for dynamic equations on time scales, we refer to the introductory book on time scales by M. By a time scale we mean a nonempty closed subset of. In recent past a new theory is emerged to unify the results not only on continuous and discrete time dynamical systems but also on discrete time dynamical system for any jump. There are many results on continuous time dynamical systems which are needed in discrete time context. The theory of linear differential equations provides a broad mathematical basis for an understanding of continuous time dynamic processes. The study of solutions of linear differential equations on time scales gained momentum because of unified approach nature for differential and difference systems. Key words: Time scale, dynamical equation, fundamental matrix, eigenvalues, eigenvectors. We develop the procedure to compute fundamental matrices for vector differential equations on time scales. ![]() This paper presents the criterion to construct fundamental matrices for the- system of linear differential equations with constant coefficients on time scales. MuraliÄepartment of Engineering Mathematics, Andhra University, Visakhapatnam, 530003, Andhra Pradesh India. Theory of System of Linear Differential Equations on Time Scales
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