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<p>In this paper, the time-fractional order Belousov-Zhabotinsky (BZ) reaction system is studied mathematically within the framework of conformable fractional derivative to characterize the memory and hereditary features in oscillatory chemical kinetics. Two efficient semi-analytical methods, the Conformable Elzaki Adomian Decomposition Method (CEADM) and Consfomable Fractional Reduced Differential Transform Method (CFRDTM) which avoid the analytical complexities due to strong nonlinearity in the system are proposed and investigated. The selection of the Elzaki transform permits fast computation of time-fractional terms due to its better convergence and handling with fractional operators when compared to classical Laplace-type transforms. A convergence theorem and error estimates are established in the Banach space showing that the solutions obtained are reliable and stable. Numerical results and graphical simulations show that both methods are accurate compared with the exact solutions for different fractional orders <i>α</i> with small absolute errors. Oscillatory dynamics are investigated for different fractional order, showing crossover between memory-dependent and classical behaviors. Comparative analyses show the computational efficiency and rapid convergence rate of CEADM compared with CFRDTM. In general, the presented conformable-based method provides a reliable, efficient as well as accurate approach for simulating fractional systems arising in chemical and physical sciences.</p>

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Mathematical analysis of time-fractional Belousov-Zhabotinsky reaction system using conformable Elzaki Adomian decomposition and reduced differential transform methods

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月4日

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  • Mohammad Alshammari,
  • Saleh Alshammari

摘要

In this paper, the time-fractional order Belousov-Zhabotinsky (BZ) reaction system is studied mathematically within the framework of conformable fractional derivative to characterize the memory and hereditary features in oscillatory chemical kinetics. Two efficient semi-analytical methods, the Conformable Elzaki Adomian Decomposition Method (CEADM) and Consfomable Fractional Reduced Differential Transform Method (CFRDTM) which avoid the analytical complexities due to strong nonlinearity in the system are proposed and investigated. The selection of the Elzaki transform permits fast computation of time-fractional terms due to its better convergence and handling with fractional operators when compared to classical Laplace-type transforms. A convergence theorem and error estimates are established in the Banach space showing that the solutions obtained are reliable and stable. Numerical results and graphical simulations show that both methods are accurate compared with the exact solutions for different fractional orders α with small absolute errors. Oscillatory dynamics are investigated for different fractional order, showing crossover between memory-dependent and classical behaviors. Comparative analyses show the computational efficiency and rapid convergence rate of CEADM compared with CFRDTM. In general, the presented conformable-based method provides a reliable, efficient as well as accurate approach for simulating fractional systems arising in chemical and physical sciences.