Comparison of Integer-, Constant-, and Variable-Order Fractional Models of Competition for Student Population Using Caputo–Fabrizio Fractional Derivative With Policy Interventions

Kiprotich Ezra Bett, Cyrus Gitonga Ngari and Grace Gakii Muthuri

International Journal of Mathematics and Mathematical Sciences, 2026, vol. 2026, 1-33

Abstract: 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

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:4337048

DOI: 10.1155/ijmm/4337048

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