Initial-boundary value problems for multi-term time-fractional wave equations

Abstract

In this paper, we deal with the well-posedness and the long-time behavior of the initial-boundary value problems for the multi-term Caputo time-fractional wave equations. First, by proving a new property concerned with the boundedness of the multivariate Mittag-Leffler functions, the unique existence of the weak solution is established. Also, we show that the solution depends on the parameters of the equation in a continuous way. In addition, the $$H^{2}$$ -decay rate of the solution is represented in terms of some orders of the fractional derivative.