Kholmat Shadimetov

Optimal Methods for Approximating the Riemann–Liouville Fractional Integral in the Sobolev Space

We construct and analyze optimal quadrature formulas for the right-sided Riemann–Liouville fractional integral in the Sobolev space L2(m)(t,1), using φ,φ′,…,φ(m−1) at N+1 equally spaced nodes. The analysis is carried out through the Peano kernel of the error functional, for which we give an exact closed form; this yiel...