Fractional modeling for improving scholastic performance of students with optimal control

Abstract

Students’ day-to-day activities can be influenced by internal and external factors that can cause academic turbulence. These factors vehemently impart to the setback of bad scholastic performance in an academic arena that is escalating among pupils of one of the Nigerian universities namely, KUST. The current paper is an extension and analysis of such a problem categorized as a contagious disease. The extension of the model is from a fractional viewpoint characterizing how this difficulty is escalated in the KUST campus. The new extensions of the model are in the sense of Caputo, Caputo–Fabrizio–Caputo and the Atangana–Baleanu–Caputo and the dimensionality for the parameters has been utilized. To this aim, the existence and uniqueness of the solutions of the model under consideration are proved by using the fixed point theory. Furthermore, we have also analyzed the positivity and boundedness of the solution for the proposed scholastic model with the Caputo differential operator. The fractional scholastic models unveil the persistence of the turbulence in the campus that can be predicted through the reproduction numbers. We also applied optimal control strategies to the proposed fractional model. The analysis shows that the positive change of behavior towards academic failure (u1) and proper orientation (u2) are effective measures in minimizing the problem in the compartments of below-average and weak students.