A class of time-fractional diffusion equations with generalized fractional derivatives
In this paper, we consider generalized fractional derivatives, which are characterized by a scale function and a weight function. It is proposed to replace the time variable with a new variable, associated with the scale and weight functions, which allows us to reduce the problems for equations with...
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2022
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ir-20.500.12258-197452022-06-22T07:22:01Z A class of time-fractional diffusion equations with generalized fractional derivatives Alikhanov, A. A. Алиханов, А. А. Caputo fractional derivative Erdelyi–Kober fractional derivative Fractional diffusion equation Generalized fractional derivative Hadamard fractional derivative In this paper, we consider generalized fractional derivatives, which are characterized by a scale function and a weight function. It is proposed to replace the time variable with a new variable, associated with the scale and weight functions, which allows us to reduce the problems for equations with generalized fractional derivatives to problems for equations with the usual fractional derivative. The equations obtained after the above change of variables are quite well studied, so that one can apply well-known effective numerical methods and use the reverse substitution to find solutions to the original problems. 2022-06-22T07:21:22Z 2022-06-22T07:21:22Z 2022 Статья Alikhanov, A. A., Huang, C. A class of time-fractional diffusion equations with generalized fractional derivatives // Journal of Computational and Applied Mathematics. - 2022. - Том 4. - Номер статьи 114424. - DOI10.1016/j.cam.2022.114424 http://hdl.handle.net/20.500.12258/19745 en Journal of Computational and Applied Mathematics application/pdf Elsevier B.V. |
| institution |
СКФУ |
| collection |
Репозиторий |
| language |
English |
| topic |
Caputo fractional derivative Erdelyi–Kober fractional derivative Fractional diffusion equation Generalized fractional derivative Hadamard fractional derivative |
| spellingShingle |
Caputo fractional derivative Erdelyi–Kober fractional derivative Fractional diffusion equation Generalized fractional derivative Hadamard fractional derivative Alikhanov, A. A. Алиханов, А. А. A class of time-fractional diffusion equations with generalized fractional derivatives |
| description |
In this paper, we consider generalized fractional derivatives, which are characterized by a scale function and a weight function. It is proposed to replace the time variable with a new variable, associated with the scale and weight functions, which allows us to reduce the problems for equations with generalized fractional derivatives to problems for equations with the usual fractional derivative. The equations obtained after the above change of variables are quite well studied, so that one can apply well-known effective numerical methods and use the reverse substitution to find solutions to the original problems. |
| format |
Статья |
| author |
Alikhanov, A. A. Алиханов, А. А. |
| author_facet |
Alikhanov, A. A. Алиханов, А. А. |
| author_sort |
Alikhanov, A. A. |
| title |
A class of time-fractional diffusion equations with generalized fractional derivatives |
| title_short |
A class of time-fractional diffusion equations with generalized fractional derivatives |
| title_full |
A class of time-fractional diffusion equations with generalized fractional derivatives |
| title_fullStr |
A class of time-fractional diffusion equations with generalized fractional derivatives |
| title_full_unstemmed |
A class of time-fractional diffusion equations with generalized fractional derivatives |
| title_sort |
class of time-fractional diffusion equations with generalized fractional derivatives |
| publisher |
Elsevier B.V. |
| publishDate |
2022 |
| url |
https://dspace.ncfu.ru/handle/20.500.12258/19745 |
| work_keys_str_mv |
AT alikhanovaa aclassoftimefractionaldiffusionequationswithgeneralizedfractionalderivatives AT alihanovaa aclassoftimefractionaldiffusionequationswithgeneralizedfractionalderivatives AT alikhanovaa classoftimefractionaldiffusionequationswithgeneralizedfractionalderivatives AT alihanovaa classoftimefractionaldiffusionequationswithgeneralizedfractionalderivatives |
| _version_ |
1760600621840334848 |