Counterexample of Local Fractional Order Chain Rule and Modified Definition of Local Fractional Order  

作　　者：FAN Kai ZHOU Cunlong 范凯;周存龙(Engineering Research Center of Heavy Machinery Ministry of Education, Taiyuan University of Science and Technology,Taiyuan 030024, China;School of Mechanical Engineering, Taiyuan University of Science and Technology,Taiyuan 030024, China;Shanxi Provincial Key Laboratory of Metallurgical Device Design Theory and Technology, Taiyuan University of Science and Technology,Taiyuan 030024, China;School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China)

机构地区：[1]Engineering Research Center of Heavy Machinery Ministry of Education,Taiyuan University of Science and Technology,Taiyuan030024,China [2]School of Mechanical Engineering,Taiyuan University of Science and Technology,Taiyuan 030024,China [3]Shanxi Provincial Key Laboratory of Metallurgical Device Design Theory and Technology,Taiyuan University of Science and Technology,Taiyuan 030024,China [4]School of Applied Science,Taiyuan University of Science and Technology,Taiyuan 030024,China

出　　处：《Journal of Donghua University(English Edition)》2020年第6期521-525,共5页东华大学学报（英文版）

基　　金：Major Science and Technology Project in Shanxi Province of China(Nos.20181101008 and 20181102015);Supplementary Platform Project of“1331”Project in Shanxi Province in 2018,China。

摘　　要：Fractional calculus is a powerful tool for modeling nonlinear systems.It is necessary to discuss the basic properties of fractional order before solving a fractional order model.Using the formula of power function defined by local fractional derivative and the chain rule to calculate a compound function,the results are inconsistent.This shows that the chain rule of local fractional derivatives similar to classical calculus is suspicious,and fractional complex transformation based on the chain rule is also suspicious and needs further discussion.In order to overcome this inconsistency,an improved definition of local fractional derivative,which can be regarded as a fractal derivative,is proposed based on the results derived from the relationship between the mass function and the Hausdorff measure.

关 键 词：local fractional order chain rule fractional complex transformation fractal derivative 

分 类 号：O172.1[理学—数学]