A New Fractional Order School Academic Performance Model and Numerical Solutions

Academic achievement is defined as the degree to which a student has achieved a learning goal. It is typically measured through the utilisation of examinations, continuous assessments and grade point averages. The student’s apprehension of failure can result in the accumulation of stress over time, which can consequently lead to a decline in academic achievement. Conversely, factors such as inadequate cognitive abilities, negative parental influence, familial circumstances and the physical and mental health of the child have been identified as the primary contributors to academic achievement. The present study proposes a novel fractional order mathematical model of academic achievement, comprising three compartments: students with above average achievement (S ), students with average achievement (M) and students with below average achievement (B). The Caputo derivative definition was employed as the fractional derivative and a stability analysis of the fractional model was conducted. Numerical solutions were obtained via the Generalized Euler Method and their graphs were drawn.