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

Alexey Zhokh and Peter Strizhak

Advances in Mathematical Physics, 2023, vol. 2023, issue 1

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.

Date: 2023
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https://doi.org/10.1155/2023/6646284

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2023:y:2023:i:1:n:6646284

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