Lie symmetry analysis and similarity reductions for the tempered-fractional Keller Segel system
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916949830664192 |
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| author | Haghighatdoost, Ghorbanali Bazghandi, Mustafa |
| author_facet | Haghighatdoost, Ghorbanali Bazghandi, Mustafa |
| contents | We perform a Lie symmetry analysis on the tempered-fractional Keller Segel (TFKS) system, a chemo-taxis model incorporating anomalous diffusion. A novel approach is used to handle the nonlocal nature of tempered fractional operators. By deriving the full set of Lie point symmetries and identifying the optimal one-dimensional subalgebras, we reduce the TFKS PDEs to ordinary differential equations (ODEs), yielding new exact solutions. These results offer insights into the long-term behavior and aggregation dynamics of the TFKS model and present a methodology applicable to other tempered fractional differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lie symmetry analysis and similarity reductions for the tempered-fractional Keller Segel system Haghighatdoost, Ghorbanali Bazghandi, Mustafa Mathematical Physics Analysis of PDEs Optimization and Control We perform a Lie symmetry analysis on the tempered-fractional Keller Segel (TFKS) system, a chemo-taxis model incorporating anomalous diffusion. A novel approach is used to handle the nonlocal nature of tempered fractional operators. By deriving the full set of Lie point symmetries and identifying the optimal one-dimensional subalgebras, we reduce the TFKS PDEs to ordinary differential equations (ODEs), yielding new exact solutions. These results offer insights into the long-term behavior and aggregation dynamics of the TFKS model and present a methodology applicable to other tempered fractional differential equations. |
| title | Lie symmetry analysis and similarity reductions for the tempered-fractional Keller Segel system |
| topic | Mathematical Physics Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2509.11690 |