Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682211120200401Diamond-$\phi_h$ dynamics on time scales with an application to economics277290427610.22075/ijnaa.2020.19155.2059ENFagbemigun OpeyemiDepartment of Mathematics, Faculty of Science, University of Lagos, Akoka, NigeriaMogbademu AlaoDepartment of Mathematics, Faculty of Science, University of Lagos, Lagos, Nigeria0000-0002-9978-2043Olaleru OlajiireDepartment of Mathematics, Faculty of Science, University of Lagos, Lagos, NigeriaJournal Article20191122Conventional 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.https://ijnaa.semnan.ac.ir/article_4276_d858c058f79d957edc47ab3d979b2cd4.pdf