  We introduce an efficient algorithm for computing fractional integrals and
derivatives and apply it for solving problems of the calculus of variations of
fractional order. The proposed approximations are particularly useful for
solving fractional boundary value problems. As an application, we solve a
special class of fractional Euler-Lagrange equations. The method is based on
Hale and Townsend algorithm for finding the roots and weights of the fractional
Gauss-Jacobi quadrature rule and the predictor-corrector method introduced by
Diethelm for solving fractional differential equations. Illustrative examples
show that the given method is more accurate than the one introduced in [Comput.
Math. Appl. 66 (2013), no. 5, 597--607], which uses the Golub-Welsch algorithm
for evaluating fractional directional integrals.
