Linear Time-Varying Dynamic-Algebraic Equations of Index One on Time Scales

In this paper, we introduce a class of linear time-varying dynamic-algebraic equations (LTVDAE) of tractability index one on arbitrary time scales. We propose a procedure for the decoupling of the considered class LTVDAE. Explicit formulae are written down both for transfer operator and the obtained decoupled system. A projector approach is used to prove the main statement of the paper and sufficient conditions of decoupling are also written down explicitly.