%0 Journal Article
%T Diamond-Phi_h dynamics on time scales with an application to economics
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Opeyemi, Fagbemigun
%A Alao, Mogbademu
%A Olajiire, Olaleru
%D 2020
%\ 01/01/2020
%V 11
%N 1
%P 277-290
%! Diamond-Phi_h dynamics on time scales with an application to economics
%K time scales
%K $phi_{h}$-concave
%K diamond-$phi_{h}$
%K Hermite-Hadamard
%K dynamic model
%R 10.22075/ijnaa.2020.19155.2059
%X Conventional dynamic models in economics are usually expressed in discrete or continuous time. A new modelling technique-time scales calculus-unifies both of these approaches into a general framework. We present and construct a dynamic optimization problem from economics in which the utility function is $phi_{h}$-concave and 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-$phi_{h}$ dynamic calculus by the authors [12] on time scales, to obtain a solution. The Hermite-Hadamard inequality with the diamond-$phi_{h}$ dynamic integral follows a proof of the new model. The new diamond-$phi_{h}$ time scale model unifies various related existing models involving general and more complex time domains.
%U https://ijnaa.semnan.ac.ir/article_4276_d858c058f79d957edc47ab3d979b2cd4.pdf