new general integral transform on time scales

In this paper, we introduce  a single integral transform that  defines all known time scales generalized integral transforms in the family of laplace transform as the new general integral transform on time scales. as a result, a unified approach is developed for the use of integral transforms representing the family of laplace transform for solving problems on continuous and discrete cases dynamics. the convergence  conditions and some principal properties accompanying the convolution theorem are given. it is shown that all generalized integral transforms on time scales included in the family of the laplace transform are special cases of a new general integral transform. the applicability of this transform is demonstrated by solving certain ordinary dynamic equations and integral equations.