Approximation with Riemann-Liouville fractional derivatives

In this article we study quantitatively with rates the pointwise convergence of a sequence of positive sublinear operators to the unit operator over continuous functions. This takes place under low order smothness, less than one, of the approximated function and it is expressed via the left and right Riemann-Liouville fractional derivatives of it. The derived related inequalities in their right hand sides contain the moduli of continuity of these fractional derivatives and they are of Shisha-Mond type. We give applications to Bernstein Max-product operators and to positive sublinear comonotonic operators connecting them to Choquet integral.