Approximation of Riemann–Liouville type integrals on an interval by methods based on Fourier–Chebyshev sums

We study approximations of Riemann–Liouville type integrals on the interval $[-1,1]$. The approximation method involves an operator constructed by replacing the density of the integral with partial sums of Fourier–Chebyshev series. Integral representations and estimates of these approximations are established for the cases in which the density belongs to some classes of continuous functions. The estimates substantially depend on the position of the point on the interval.