Best Approximations of Solutions of Fractional-integral Equations with the Riemann-Liouville Operator

The article is devoted to the best approximations of solutions of integral equations that are defined on the line segment and have a fractional Riemann-Liouville integral in the main part. These approximations are constructed with the “generalized” projection method using the apparatus of algebraic polynomials. At the same time, the Fredholm property of an integral equation operator in a special pair of Hölder spaces of the desired elements and right-hand sides plays an important role.