NON-HOMOGENEOUS FRACTIONAL BOUNDARY VALUE PROBLEM IN SPACES OF GENERALIZED FUNCTIONS

Анотація

We prove the existence and uniqueness theorem and get the representation, by means of the Green vector-function, of the solution of the problem

$u_t^{\left(\beta \right)}(x,t)-a^2\Delta u(x,t)=F(x,t), (x,t)\in \Omega \times (0,T], a=const$

$u(x,t)=F_1(x,t), (x,t)\in \partial \Omega \times (0,T], u(x,t)=F_2\left(x\right), x\in \Omega$

with Riemann-Liouville fractional derivative $u_t^{\left(\beta \right)}$ of the order $\beta \in (0,1)$ and $F$, $F_1$, $F_2$ from spaces of generalized functions $D\text{'}$.