Diamond- ϕh dynamics on time scales with an Application to Economics

Conventional dynamic models in economics are usually expressed in discrete or continuous time. a new modelling technique-time scale calculus-unifies both of these approaches into a general framework. in this paper, we present and construct a dynamic optimization problem from economics in which the utility function is ϕh-concave, the value function and constraints are on different time scales. the calculus of variations and optimal control are employed, with the aid of the newly introduced diamond-ϕh dynamic calculus by the authors [12] on time scales, to obtain a solution. the hermite-hadamard inequality with the diamond-ϕh dynamic integral on time scales, follows a proof of the new model. the new diamond-ϕh time scale model unify various related existing models involving general and more complex time domains.