This study develops constant‐order (CO) and variable‐order (VO) Caputo–Fabrizio (CF) fractional derivative (CFFD) models to extend the classical integer‐order framework for analyzing competition among public, private, and nonenrolled student populations under varying policy intervention intensities. Existence and uniqueness of solutions were confirmed using fixed‐point theorems, and stability was assessed through Jacobian analysis at the trivial and coexistence equilibrium points, which proved to be unstable and stable, respectively, under moderate policy interventions. A modified two‐step Adams–Bashforth scheme was implemented in MATLAB software to generate stable and convergent simulations. Numerical results demonstrate that both the fractional order and policy intervention intensity strongly influence long‐term system behavior: Weak intervention ( p < 0.914) produces instability, marked by rapid public school expansion, declining private school enrollment, and rising nonenrollment, whereas adequate interventions ( p ≥ 0.914), particularly under stronger memory effects ( α = 0.6, 0.7, and 0.8), guide the system toward asymptotic stability. Comparative analysis shows that the VO–CFFD model provides superior robustness, faster convergence, and higher accuracy than both the CO–CFFD and integer‐order models. These findings highlight the potential of VO fractional modeling as a powerful predictive and policy design tool for strengthening education systems and supporting progress toward SDG 4.
Bett et al. (Thu,) studied this question.