Regularity of the solutions of the boundary value problems for diffusion-wave equation with generalized functions in right-hand sides - Lopushansky, A.O. (Carpathian Mathematical Publications, 2013)
We prove the unique solvability of the first boundary value problem of equation $$u^{(β)}_t-a(t)Δ u=F(x,t), \;\;\; (x,t) \in (0,l)× (0,T],$$ with Riemann-Liouville fractional derivative $u^{(β)}_t$ of the order $β\in (0,2)$, 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 $t$.