Boundedness and exponential stabilization for time-space fractional parabolic-elliptic Keller-Segel model in higher dimensions

We consider initial boundary value problem for the time-space fractional parabolic- elliptic Keller-Segel model{C0D beta tu=-(-triangle)alpha 2(rho(v)u) (t,x)is an element of(0,T]x ohm (-triangle) alpha 2 v + v = u, (t, x) E (0, T] x ohm in a bounded domain ohm C R-n(n > 3) with smooth boundary, where beta E (0, 1), alpha E (1, 2) and rho stands for a signal-dependent motility. It is shown that for some special initial datum, there exists the uniform-in-time upper bound for v such that the associated initial-boundary system possesses a global classical solution which is uniformly bounded. Moreover, building on this boundedness property, it is proved that the exponential stabilization of the classical solution. (c) 2023 Elsevier Ltd. All rights reserved.