A note on the matrix solutionof the problem XΔ = AX, X(t0) = I

In this note, we give an interesting representation of the matrix solution of the initial problem XΔ = AX, X(t0) = I on time scales. Our approach does not require to compute eigenvalues of matrix A, but we are limited on time scales, which are, in a sense, not more complicated than the middle-third Cantor set.