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.

In this paper some new Hardy–type inequalities on Time scales are derived and proved using the concept of superquadratic functions. Also, we extend Hardy–type inequalities involving superquadratic functions with general kernels to the case with arbitrary Time scales. Several consequences of our results are given and their connection with recent results in the literature are pointed out and discussed.

In this paper, we present a generalization of the Montgomery Identity to various Time scale versions, including the discrete case, continuous case, and the case of quantum calculus. By obtaining this generalization of Montgomery Identity  we establish results about the generalization of Ostrowski-Gr\"{u}ss like inequality to the several Time scales, namely discrete case, continuous case and the case of quantum calculus. Additionally, we recapture several published results from different authors in various papers, thus unifying the corresponding discrete and continuous versions. Furthermore, we demonstrate the applicability of our derived consequence to the case of quantum calculus.

In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on Time scales. Using the derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. We present some examples to illustrate our results.

In this study, existence of positive solutions are considered for second order boundary value problems on any Time scales even in the case when y ,0 may also be a solution.

Conventional dynamic models in Economics are usually expressed in discrete or continuous Time. A new modelling technique-Time scale calculus-uni es both of these approaches into a general frame-work. In this paper, we present and construct a dynamic Optimization problem from economics in which the utility function is  h-concave, the value function and constraints are on di erent Time scales. The calculus of variations and optimal control are employed, with the aid of the newly in-troduced diamond- h dynamic calculus by the authors [12] on Time scales, to obtain a solution. The Hermite-Hadamard inequality with the diamond- h dynamic integral on Time scales, follows a proof of the new model. The new diamond- h Time scale model unify various related existing models involving general and more complex Time domains.