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.
Opeyemi,F , Alao,M and Olajiire,O . (2020). Diamond-$\phi_h$ dynamics on time scales with an application to economics. International Journal of Nonlinear Analysis and Applications, 11(1), 277-290. doi: 10.22075/ijnaa.2020.19155.2059
MLA
Opeyemi,F , , Alao,M , and Olajiire,O . "Diamond-$\phi_h$ dynamics on time scales with an application to economics", International Journal of Nonlinear Analysis and Applications, 11, 1, 2020, 277-290. doi: 10.22075/ijnaa.2020.19155.2059
HARVARD
Opeyemi F, Alao M, Olajiire O. (2020). 'Diamond-$\phi_h$ dynamics on time scales with an application to economics', International Journal of Nonlinear Analysis and Applications, 11(1), pp. 277-290. doi: 10.22075/ijnaa.2020.19155.2059
CHICAGO
F Opeyemi, M Alao and O Olajiire, "Diamond-$\phi_h$ dynamics on time scales with an application to economics," International Journal of Nonlinear Analysis and Applications, 11 1 (2020): 277-290, doi: 10.22075/ijnaa.2020.19155.2059
VANCOUVER
Opeyemi F, Alao M, Olajiire O. Diamond-$\phi_h$ dynamics on time scales with an application to economics. IJNAA. 2020;11(1):277-290. doi: 10.22075/ijnaa.2020.19155.2059
International Journal of Nonlinear Analysis and Applications