  In the present paper, a generalized local Taylor formula with the local
fractional derivatives (LFDs) is proposed based on the local fractional
calculus (LFC). From the fractal geometry point of view, the theory of local
fractional integrals and derivatives has been dealt with fractal and
continuously non-differentiable functions, and has been successfully applied in
engineering problems. It points out the proof of the generalized local
fractional Taylor formula, and is devoted to the applications of the
generalized local fractional Taylor formula to the generalized local fractional
series and the approximation of functions. Finally, it is shown that local
fractional Taylor series of the Mittag-Leffler type function is discussed.
