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

作者机构：Engineering Research Center of Heavy Machinery Ministry of EducationTaiyuan University of Science and TechnologyTaiyuan030024China School of Mechanical EngineeringTaiyuan University of Science and TechnologyTaiyuan 030024China Shanxi Provincial Key Laboratory of Metallurgical Device Design Theory and TechnologyTaiyuan University of Science and TechnologyTaiyuan 030024China School of Applied ScienceTaiyuan University of Science and TechnologyTaiyuan 030024China 

出 版 物：《Journal of Donghua University(English Edition)》 (东华大学学报（英文版）)

年 卷 期：2020年第37卷第6期

页      面：521-525页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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 

主　　题：local fractional order chain rule fractional complex transformation fractal derivative 

摘      要：Fractional calculus is a powerful tool for modeling nonlinear *** is necessary to discuss the basic properties of fractional order before solving a fractional order *** the formula of power function defined by local fractional derivative and the chain rule to calculate a compound function,the results are *** 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 *** 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.