On Diamond-Alpha Dynamic Equations and Inequalities

In view of the recently developed theory of calculus for dynamic equations on time scales (which unifies discrete and continuous systems), in this project we give some of the basics of the extension of the theory to the combined delta (forward) and nabla (backward) derivatives. In this set up the newly developed theory of diamond-alpha derivatives are analyzed through some equation and inequality properties. In particular Opial type Diamond-alpha dynamic Inequalities are discussed in this context and recently developed results and their improved versions are given in this work