Regularity of the solutions of the boundary value problems for diffusion-wave equation with generalized functions in right-hand sides

Abstract

We prove the unique solvability of the first boundary value problem of equation
$$u^{(\beta)}_t-a(t)\Delta u=F(x,t), \;\;\; (x,t) \in (0,l)\times
(0,T],$$

with Riemann-Liouville fractional derivative $u^{(\beta)}_t$ of the order $\beta\in (0,2)$, positive smooth coefficient $a(t)$ and generalized functions in right-hand sides. We obtain some sufficient conditions of the regularity of its solution as variable $t$.