Numerical Treatment for a Novel Crossover Chemical Reactor Mathematical Model

N. H. Sweilam, S. M. Al-Mekhlafi, A. R. Swidan, E. M. Abo-Eldahab and A. S. Deif

International Journal of Mathematics and Mathematical Sciences, 2026, vol. 2026, 1-19

Abstract: This paper introduces a novel fractional crossover chaotic system derived from a chemical reactor model, providing a unified framework that simultaneously captures classical and memory-dependent dynamics. The principal contributions include the formulation of a hybrid mathematical model integrating integer–fractional and fractional–integer dynamics, alongside the development of the CPC-NSAB5 numerical scheme, which enables accurate and efficient computation of fractional differential equations with a demonstrated convergence rate of 1.034, and the key finding that fractional-order memory effects markedly suppress chaotic intensity evidenced by a reduction in the maximum Lyapunov exponent from λmax=0.38938 in the integer-order case to λmax≈0 at ζ=0.88. Nonlinear transitions are further characterized via bifurcation diagrams, phase portraits, and quantitative measures including energy and entropy. Results confirm that the proposed crossover scheme offers a stable, accurate, and computationally efficient approach for modeling complex chemical reactor systems, with the fractional order emerging as a critical parameter for tuning chaotic behavior.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:2528691

DOI: 10.1155/ijmm/2528691

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