Stochastic Representation and Monte Carlo Simulation for Multiterm Time-Fractional Diffusion Equation
In this paper, we mainly study the solution and properties of the multiterm time-fractional diffusion equation. First, we obtained the stochastic representation for this equation, which turns to be a subordinated process. Based on the stochastic representation, we calculated the mean square displace...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/1315426 |
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| author | Longjin Lv Luna Wang |
| author_facet | Longjin Lv Luna Wang |
| author_sort | Longjin Lv |
| collection | DOAJ |
| description | In this paper, we mainly study the solution and properties of the multiterm time-fractional diffusion equation. First, we obtained the stochastic representation for this equation, which turns to be a subordinated process. Based on the stochastic representation, we calculated the mean square displacement (MSD) and time average mean square displacement, then proved some properties of this model, including subdiffusion, generalized Einstein relationship, and nonergodicity. Finally, a stochastic simulation algorithm was developed for the visualization of sample path of the abnormal diffusion process. The Monte Carlo method was also employed to show the behavior of the solution of this fractional equation. |
| format | Article |
| id | doaj-art-4949af0e747c404fb39fbf8ca5be5dc8 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-4949af0e747c404fb39fbf8ca5be5dc82025-02-03T05:49:53ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/13154261315426Stochastic Representation and Monte Carlo Simulation for Multiterm Time-Fractional Diffusion EquationLongjin Lv0Luna Wang1School of Finance and Information, Ningbo University of Finance and Economics, Ningbo 315000, ChinaSchool of Finance and Information, Ningbo University of Finance and Economics, Ningbo 315000, ChinaIn this paper, we mainly study the solution and properties of the multiterm time-fractional diffusion equation. First, we obtained the stochastic representation for this equation, which turns to be a subordinated process. Based on the stochastic representation, we calculated the mean square displacement (MSD) and time average mean square displacement, then proved some properties of this model, including subdiffusion, generalized Einstein relationship, and nonergodicity. Finally, a stochastic simulation algorithm was developed for the visualization of sample path of the abnormal diffusion process. The Monte Carlo method was also employed to show the behavior of the solution of this fractional equation.http://dx.doi.org/10.1155/2020/1315426 |
| spellingShingle | Longjin Lv Luna Wang Stochastic Representation and Monte Carlo Simulation for Multiterm Time-Fractional Diffusion Equation Advances in Mathematical Physics |
| title | Stochastic Representation and Monte Carlo Simulation for Multiterm Time-Fractional Diffusion Equation |
| title_full | Stochastic Representation and Monte Carlo Simulation for Multiterm Time-Fractional Diffusion Equation |
| title_fullStr | Stochastic Representation and Monte Carlo Simulation for Multiterm Time-Fractional Diffusion Equation |
| title_full_unstemmed | Stochastic Representation and Monte Carlo Simulation for Multiterm Time-Fractional Diffusion Equation |
| title_short | Stochastic Representation and Monte Carlo Simulation for Multiterm Time-Fractional Diffusion Equation |
| title_sort | stochastic representation and monte carlo simulation for multiterm time fractional diffusion equation |
| url | http://dx.doi.org/10.1155/2020/1315426 |
| work_keys_str_mv | AT longjinlv stochasticrepresentationandmontecarlosimulationformultitermtimefractionaldiffusionequation AT lunawang stochasticrepresentationandmontecarlosimulationformultitermtimefractionaldiffusionequation |