Lie symmetry analysis and similarity reductions for the tempered-fractional Keller Segel system

2025/09/15 by Ghorbanali Haghighatdoost, Haghighatdoost, Ghorbanali, Mustafa Bazghandi +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #MRI in cancer diagnosis #Mathematical Biology Tumor Growth #Mathematical Physics (math-ph) #Microtubule and mitosis dynamics #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2509.11690

openalex publication_date 2025/09/15 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Existence and regularity of the fractional Keller–Segel equation via the extended theory of semigroups

Cited by

• Geometric Dynamical Systems

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