A FRACTIONAL-ORDER OPTIMAL CONTROL MODEL FOR EXAMINATION MALPRACTICE IN GREEN SMART SCHOOLS

Abstract

The Green Smart School Initiative is a concept that seeks to promote sustainable practices in schools.  The idea is to integrate green technology, energy efficiency, and environmental education into the school environment.  In this study, a fractional order examination malpractice optimal control model for the effective implementation of green smart school initiative in the sense of Caputo is formulated.  The host population is divided into five mutually exclusive compartments of susceptible, malpractice, punished or disciplined, recovered and resistant individuals. The positivity, existence and uniqueness result of the model were established, and the two equilibria, that is, the malpractice free and malpractice presence equilibrium solutions of the model in the presence of effective examination malpractice control strategies for the green smart school initiative are presented. The graphical representation showing the basic reproduction number when less than unity is is displayed. Simulations involving the effectiveness of the control strategies in prevention and control of examination malpractice for the smooth implementation of the green smart school initiatives are observed. In addition, we graphically illustrate the optimal control of the strategies with numerical technique of fractional multi-Stage Differential Transform Method via Matlab which showed that the control strategies is capable of preventing and controlling examination malpractice and subsequently facilitating the effective implementation of green smart school initiativ