Diamond-$\phi_h$ dynamics on time scales with an application to economics

Document Type : Research Paper


1 Department of Mathematics, Faculty of Science, University of Lagos, Akoka, Nigeria

2 Department of Mathematics, Faculty of Science, University of Lagos, Lagos, Nigeria


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.


Volume 11, Issue 1
April 2020
Pages 277-290
  • Receive Date: 22 November 2019
  • Revise Date: 08 January 2020
  • Accept Date: 02 February 2020
  • First Publish Date: 01 April 2020