Journal of Shanghai University(Natural Science Edition) ›› 2021, Vol. 27 ›› Issue (6): 1149-1161.doi: 10.12066/j.issn.1007-2861.2257

• Research Articles • Previous Articles     Next Articles

Asymptotics and large time behavior of solutions to a type of time-space fractional wave equation

LI Zhiqiang1,2()   

  1. 1. College of Sciences, Shanghai University, Shanghai 200444, China
    2. Department of Mathematics, Lüliang University, Lüliang 033001, Shanxi, China
  • Received:2020-05-08 Online:2021-12-31 Published:2020-09-23
  • Contact: LI Zhiqiang E-mail:lizhiqiang0914@126.com

Abstract:

This study investigates the asymptotic behaviors of a solution to time-space fractional partial differential equation with the fractional Laplacian, where the time fractional derivative is in the sense of Caputo, with the order $\alpha\in(1,2)$. By using the properties of the Fox $H$-function and Young's inequality, gradient estimates and large time behavior of the solution are obtained.

Key words: Caputo derivative, fractional Laplacian, asymptotic behavior, large time behavior

CLC Number: