On a Riemann-Liouville Generalized Taylor's Formula

Abstract

In this paper, a generalized Taylor's formula of the kindfx=∑j=0najx-a(j+1)α-1+T nx,whereaj∈R,xa, 0≤α≤1, is established. Such expression is precisely the classical Taylor's formula in the particular case α=1. In addition, detailed expressions forTn(x) andaj, involving the Riemann-Liouville fractional derivative, and some applications are also given. © 1999 Academic Press.