On investigation of the mathematical model depicting the transition from temporary to permanent mathematics anxiety via piecewise fractional differential equations

Abstract

The focus of this study is on a mathematical model that incorporates anxiety about math among students, specifically looking at a scenario where a group of students who are not anxious initially develop anxiety over time, i.e. a class with persistent anxiety is added to the population after some time. The addition of students with permanent anxiety after a while to a population means adding a new state variable to the system of differential equations after a certain time, which offers a different perspective on a new class of differential equations called piecewise differential equations. New examinations are intended to be introduced for a piecewise differential equation by examining analyses like the piecewise spread rate of anxiety and anxiety endemic/anxiety free equilibrium points. The graphical illustrations are simulated to represent outcomes of piecewise differential equations with integer and non-integer orders. It is our belief that this class of differential equations will inject fresh perspectives into modeling, resulting in valuable additions to scholarly works and paving the way for innovative research opportunities.