Numerical Treatment for a Novel Crossover Chemical Reactor Mathematical Model

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.