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Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion Equation

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  • Alexey Zhokh
  • Peter Strizhak
  • Zine El Abiddine Fellah

Abstract

The time-fractional diffusion equation coupled with a first-order irreversible reaction is investigated by employing integral transforms. We derive Green’s functions for short and long times via approximations of the Mittag-Leffler function. The time value for which the crossover between short- and long-time asymptotic holds is presented in explicit form. Based on the developed Green’s functions, the exact analytic asymptotic solutions of the time-fractional reaction-diffusion equation are obtained. The applicability of the obtained solutions is demonstrated via quantification of the reaction-diffusion kinetics during heterogeneous catalytic chitin conversion to chitosan.

Suggested Citation

  • Alexey Zhokh & Peter Strizhak & Zine El Abiddine Fellah, 2023. "Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion Equation," Advances in Mathematical Physics, Hindawi, vol. 2023, pages 1-6, April.
    • Handle: RePEc:hin:jnlamp:6646284
    DOI: 10.1155/2023/6646284
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