Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion Equation
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...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2023/6646284 |
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| author | Alexey Zhokh Peter Strizhak |
| author_facet | Alexey Zhokh Peter Strizhak |
| author_sort | Alexey Zhokh |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-bca5ca238b31498ababa665e792453f1 |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-bca5ca238b31498ababa665e792453f12025-02-03T06:42:51ZengWileyAdvances in Mathematical Physics1687-91392023-01-01202310.1155/2023/6646284Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion EquationAlexey Zhokh0Peter Strizhak1L.V. Pisarzhevskii Institute of Physical Chemistry of National Academy of Sciences of UkraineL.V. Pisarzhevskii Institute of Physical Chemistry of National Academy of Sciences of UkraineThe 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.http://dx.doi.org/10.1155/2023/6646284 |
| spellingShingle | Alexey Zhokh Peter Strizhak Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion Equation Advances in Mathematical Physics |
| title | Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion Equation |
| title_full | Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion Equation |
| title_fullStr | Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion Equation |
| title_full_unstemmed | Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion Equation |
| title_short | Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion Equation |
| title_sort | green s functions on various time scales for the time fractional reaction diffusion equation |
| url | http://dx.doi.org/10.1155/2023/6646284 |
| work_keys_str_mv | AT alexeyzhokh greensfunctionsonvarioustimescalesforthetimefractionalreactiondiffusionequation AT peterstrizhak greensfunctionsonvarioustimescalesforthetimefractionalreactiondiffusionequation |