University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 17 2 2026 06 01 Extended Fractional-Time Oregonator Model Accounting for Proton Dynamics 137 177 115564 10.22052/ijmc.2025.257706.2074 EN Sarita Pippal Department of Mathematics‎, ‎Panjab University‎, ‎Chandigarh‎, ‎India Journal Article 2025 10 04 ‎In this manuscript‎, ‎we develop a generalized form of the classical three-variable Oregonator model by‎ ‎extending it to a four--dimensional fractional-order system‎. ‎The extended formulation explicitly includes‎ the proton concentration $\mathcal{H}(t)$ within the Belousov-Zhabotinsky (BZ) reaction kinetics and‎ introduces memory effects through the Caputo fractional derivative of order‎ $\alpha\in(0,1]$‎. ‎For the classical case $\alpha = 1$‎, ‎the model reduces to an ordinary differential‎ equation system‎, ‎which is solved using the third-order Adams-Bashforth-Moulton (ABM3) predictor-corrector‎ ‎method and compared with the standard fourth-order Runge-Kutta (RK4) scheme‎. For $0 <\alpha<1$‎, ‎the system is numerically integrated using the fractional ABM3 method‎, ‎where the Caputo derivative is discretized by‎ means of convolution-type memory weights‎. Numerical experiments reveal that both proton feedback‎ plays a crucial role in shaping the oscillatory dynamics and stabilizing the long-term behavior‎. Analytical results further confirm positivity and boundedness of the solutions‎, ‎characterize the equilibrium‎ ‎points‎, ‎and determine their stability‎. ‎The trivial equilibrium is always unstable‎, ‎whereas the nontrivial‎ equilibrium is locally asymptotically stable under realistic parameter conditions‎. ‎Sensitivity and eigenvalue analysis additionally show that the parameters (a‎, ‎q)‎ tend to destabilize the system‎, ‎while $(\delta‎, ‎\varepsilon‎, ‎\gamma)$ enhance stability‎. Here‎, ‎a and q represent the autocatalytic and inhibition reaction strengths‎, whereas $\delta$‎, ‎$\varepsilon$‎, ‎and $\gamma$ denote the characteristic timescales‎ of the inhibitor‎, ‎autocatalyst‎, ‎and proton dynamics‎, ‎respectively‎. https://ijmc.kashanu.ac.ir/article_115564_97c1e0da98ad28ed90d7d713eeaf02c2.pdf