首页|Counterexample of Local Fractional Order Chain Rule and Modified Definition of Local Fractional Order
Counterexample of Local Fractional Order Chain Rule and Modified Definition of Local Fractional Order
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国家科技期刊平台
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维普
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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.
local fractional orderchain rulefractional complex transformationfractal derivative
FAN Kai、ZHOU Cunlong
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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
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Major Science and Technology Project in Shanxi Province of ChinaMajor Science and Technology Project in Shanxi Province of ChinaSupplementary Platform Project of"1331"Project in Shanxi Province in 2018, China
国家科技期刊平台
NSTL
维普
万方数据
