Schauder estimates for equationswith fractional derivatives
Schauder estimates for equationswith fractional derivatives
The equation \begin{equation*} D^\alpha _t (u-h_1) + D^\beta _x(u-h_2) =f,\quad 0< \alpha ,\beta < 1, \quad t,x \geq 0,\tag {$*$} \end{equation*} where $D^\alpha _t$ and $D^\beta _x$ are fractional derivatives of order $\alpha$ and $\beta$ is studied. It is shown that if $f=f(\underline {t}, \underline {x})$, $h_1=h_1(\underline {x})$, and $h_2=h_2(\underline …