Journal of Prime Research in Mathematics

Fractional Optimal Control for a Corruption model

Ebenezer Bonyah
Department of Mathematics Education, University of Education, Winneba (Kumasi Campus), Ghana.

Copyright © 2020 Ebenezer Bonyah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this work, a fractional optimal control of corruption model is investigated. The variable controls are included in the model to optimize the best strategy in reducing the corruption in the society. The fraction derivative employed in the study is in Atangana–Beleanu–Caputo (ABC) sense based on generalized Mittag–Leffler. The uniqueness and existence of solution of the corruption model is established. The necessary and sufficient condition for establishing fractional optimal control in ABC sense is determined. A numerical algorithm for obtaining fractional optimal control solution is presented. The numerical solution results show that the best strategy in controlling corruption in the society is to optimize all the thee controls simultaneously.


Corruption, fractional optimal control, Mittag–Leffler, Atangana–Beleanu–Caputo, existence and uniqueness.