  We establish a new generalized Taylor's formula for power fractional
derivatives with nonsingular and nonlocal kernels, which includes many known
Taylor's formulas in the literature. Moreover, as a consequence, we obtain a
general version of the classical mean value theorem. We apply our main result
to approximate functions in Taylor's expansions at a given point. The explicit
interpolation error is also obtained. The new results are illustrated through
examples and numerical simulations.
