| 分数阶导数的不适定性及其相关问题 |
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| 引用本文： | 詹华税,张梦杰.分数阶导数的不适定性及其相关问题[J].厦门理工学院学报,2021,29(3):77-82. |
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| 作者姓名： | 詹华税 张梦杰 |
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| 作者单位： | （厦门理工学院应用数学学院，福建 厦门361024) |
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| 摘 要： | 根据分数阶导数的定义，计算基本初等函数在Riemann Liouville分数阶导数和Caputo分数阶导数不同定义下的分数阶导数，并对同一基本初等函数不同分数阶导数进行计算，研究分数阶导数的不适定性、相容性和四则运算等问题。研究推断出基本初等函数分数阶导数随着阶数变化而变化的趋势，同时发现，分数阶导数并不具备整数阶导数的乘法和除法法则，而是具有更复杂的分析性质。
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| 关 键 词： | 分数阶导数 基本初等函数 不适定问题 Riemann Liouville Caputo |
Ill posedness of the Fractional Derivatives and Other Related Problems |
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| ZHAN Huashui,ZHANG Mengjie.Ill posedness of the Fractional Derivatives and Other Related Problems[J].Journal of Xiamen University of Technology,2021,29(3):77-82. |
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| Authors: | ZHAN Huashui ZHANG Mengjie |
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| Affiliation: | (School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China) |
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| Abstract: | To study the ill posedness,compatibility and basic arithmetic operations of fractional derivatives,the fractional derivatives of the elementary functions in the sense of Riemann Liouville fractional derivative and the Caputo fractional derivative are calculated respectively,and the different order fractional derivatives for a given elementary function calculated according to the definition of fractional derivatives.Thus,it is inferred that the fractional derivatives of a given elementary function change with the order change of the fractional derivatives,and it is found that the usual multiplication and division rule of integer order derivative does not apply to a fractional derivative,which has more complicated analysis properties. |
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| Keywords: | fractional derivativeelementary functionill posed problemRiemann LiouvilleCaputo |
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