The first boundary-value problem for a fractional diffusion-wave equation in a non-cylindrical domain

摘要

We solve the first boundary-value problem in a non-cylindrical domain for a diffusion-wave equation with the Dzhrbashyan-Nersesyan operator of fractional differentiation with respect to the time variable. We prove an existence and uniqueness theorem for this problem, and construct a representation of the solution. We show that a sufficient condition for unique solubility is the condition of Holder smoothness for the lateral boundary of the domain. The corresponding results for equations with Riemann-Liouville and Caputo derivatives are particular cases of results obtained here.