Taylor-type formulas for arbitrary continuous functions on intervals and their application in control problems for distributed systems (Q2155319)

The author provides several alternative versions of Taylor formulas on finite intervals by lowering the requirement on the differentiability of the functions approximated. One such version only requires \((n-1)\) continuous derivatives at a point and gives the error term using Dini derivatives, the next uses Bernstein polynomials and requires only continuity of the function and the third uses Caputo derivatives for the error term. The paper concludes by applying the latter two forms of approximation to a control problem for a distributed oscillatory system.