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<p>The Belousov-Zhabotinsky (BZ) reaction is a classic example of chemical oscillations, traditionally modeled with integer-order equations. Recent developments in fractional calculus have opened new possibilities for capturing memory effects and non-local dynamics in such systems. In this study, we present a time-fractional version of the Noyes-Field model for the BZ reaction, solved using the residual power series method (RPSM) and new iterative method (NIM). These approaches provide an efficient framework for handling nonlinear fractional differential equations that arise in complex chemical processes. To address fractional derivatives, we employ the conformable operator, which improves computational efficiency without sacrificing accuracy. Numerical simulations confirm the effectiveness of the proposed methods and highlight the superior ability of fractional-order models to capture oscillatory behavior in the BZ reaction. Our findings emphasize the advantages of combining fractional calculus with iterative techniques for modeling chemical systems and point to promising directions for future work in nonlinear dynamics and reaction kinetics.</p>

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A conformable operator approach to time-fractional Noyes-Field model for Belousov-Zhabotinsky reaction

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月7日

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  • Waleed Hamali,
  • Musaad S. Aldhabani,
  • Musawa Yahya Almusawa,
  • Abdullah Ali H. Ahmadini,
  • Mohammad Khalid Storai

摘要

The Belousov-Zhabotinsky (BZ) reaction is a classic example of chemical oscillations, traditionally modeled with integer-order equations. Recent developments in fractional calculus have opened new possibilities for capturing memory effects and non-local dynamics in such systems. In this study, we present a time-fractional version of the Noyes-Field model for the BZ reaction, solved using the residual power series method (RPSM) and new iterative method (NIM). These approaches provide an efficient framework for handling nonlinear fractional differential equations that arise in complex chemical processes. To address fractional derivatives, we employ the conformable operator, which improves computational efficiency without sacrificing accuracy. Numerical simulations confirm the effectiveness of the proposed methods and highlight the superior ability of fractional-order models to capture oscillatory behavior in the BZ reaction. Our findings emphasize the advantages of combining fractional calculus with iterative techniques for modeling chemical systems and point to promising directions for future work in nonlinear dynamics and reaction kinetics.