Fractional derivative of Abel type on a half-line
Fractional derivative of Abel type on a half-line
We consider the initial-boundary value problem on a half-line for an evolution equation \[ \left ( \partial _{t}+\left \vert \partial _{x}\right \vert ^{\alpha }\right ) u(x,t)=f(x,t),t>0,\ x>0, \] with a fractional derivative of Abel type \begin{equation*} \text {(0.1)\qquad \qquad \qquad \qquad \qquad }\left \vert \partial _{x}\right \vert ^{\alpha }u=\mathcal {R}^{1-\alpha …