Persistence of traveling waves to the time fractional Keller‐Segel system with a small parameter

Abstract

This paper aims to investigate the time fractional Keller‐Segel system with a small parameter. After the fractional order traveling wave transformation, the heteroclinic orbit of the degenerate time fractional Keller‐Segel system is demonstrated through the method of constructing a suitable invariant region. Moreover, the persistence of traveling waves in the system with a small parameter can be further illustrated. The results are mainly reliance on the application of geometric singular perturbation theory and Fredholm theorem, which are fundamental theoretical frameworks for dealing with problems of complexity and high dimensionality. Eventually, the asymptotic behavior is depicted by the asymptotic theory to illustrate the rate of decay for traveling waves.