On a Riemann–Liouville Generalized Taylor's Formula

In this paper, a generalized Taylor's formula of the kindfx=∑j=0najx−a(j+1)α−1+Tnx,whereaj ∈ R,x > a, 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.