On a Riemann–Liouville Generalized Taylor’s Formula*

In this paper, a generalized Taylor’s formula of the kind f x‘ D n XjD0 ajx − a‘jC1‘ −1 C Tnx‘; where aj 2 , x > a, 0 1, is established. Such expression is precisely the classical Taylor’s formula in the particular case D 1. In addition, detailed expressions for Tnx‘ and aj , involving the Riemann–Liouville fractional derivative, and some applications are also given.