一元不可微函数的局部分数阶微分的基本理论

The Fundamentals of Local Fractional Derivative of the One-variable Non-differentiable Functions

本文讨论了基于Jumarie的分数阶微积分理论的修正局部分数阶导数,推广了局部分数阶导数的基本理论,给出了局部分数阶导数的唯一性,并且证明了局部分数阶导数的罗尔定理、微分中值定理、广义的柯西中值定理及其洛必这法则。

Based on the theory of Jumarie＇s fractional calculus,local fractional derivative is modified in detail and its fundamentals of local fractional derivative are proposed in this paper. The uniqueness of local fractional derivative is obtained and the Rolle＇s theorem, the mean value theorem,the Cauchy＇s generalized mean value theorem and the L＇ Hospital＇s rules are proved.