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

Generalized Local Fractional Taylor's Formula with Local Fractional Derivative