  In this paper a fractional differential equation of the Euler-Lagrange /
Sturm-Liouville type is considered. The fractional equation with derivatives of
order $\alpha \in \left( 0,1 \right]$ in the finite time interval is
transformed to the integral form. Next the numerical scheme is presented. In
the final part of this paper examples of numerical solutions of this equation
are shown. The convergence of the proposed method on the basis of numerical
results is also discussed.
