Taylor’s Formula for Generalized Weighted Fractional Derivatives with Nonsingular Kernels

Abstract

We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and derivatives. As an application, new mean value theorems for generalized weighted fractional operators are obtained. Direct corollaries allow one to obtain the recent Taylor’s and mean value theorems for Caputo–Fabrizio, Atangana–Baleanu–Caputo (ABC) and weighted ABC derivatives.