On the convergence of difference schemes for differential equations with a fractional derivative (Q1380298)

The author gives some statements on convergence of Samarskij's type difference schemes for the boundary value problem \[ \frac{d}{dx} \left[k(x)\frac{du}{dx}\right] -r(x)D_{0x}^\alpha u - q(x)u= -f(x), \quad u(0)=u(1)=0, \] where \(k(x)\geq c_0>0, r(x)\geq 0\), \(q(x)\geq 0\) and \(D_{0x}^\alpha u\) is the Riemann-Liouville fractional derivative, \(0< \alpha <1\).