About an estimate from above of the fractional derivative of the composition of two functions

In the paper, an estimate from above of the fractional Riemann–Liouville derivative of an order $\alpha \in (0, 1)$ of the composition of two functions is proved for the case when the inner function is assumed only to be represented by the fractional Riemann–Liouville integral of a measurable essentially bounded function. The necessity of such an estimate arises in control problems of dynamical systems described by differential equations with fractional derivatives