PROPERTIES OF THE CAPUTO-FABRIZIO FRACTIONAL DERIVATIVE AND ITS DISTRIBUTIONAL SETTINGS
PROPERTIES OF THE CAPUTO-FABRIZIO FRACTIONAL DERIVATIVE AND ITS DISTRIBUTIONAL SETTINGS
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DOI：
10.1515/fca-2018-0003
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发表时间：
2018-02-01
影响因子：
3
通讯作者：
Zorica, Dusan
中科院分区：
文献类型：
--
作者：
Atanackovic, Teodor M.;Pilipovic, Stevan;Zorica, Dusan
Caputo-Fabrizio分数阶导数在经典和分布的设置进行了分析。给出了应用于线性粘弹性时所需的积分不等式。它们是由弱形式的熵不等式得到的。给出了分部积分、展开公式、逼近公式和汉密尔顿型广义变分原理。第一个原理中的汉密尔顿作用积分与分数次积分的下界不一致，而第二个原理中的极小化是关于给定空间中的函数和分数阶导数的。
The Caputo-Fabrizio fractional derivative is analyzed in classical and distributional settings. The integral inequalities needed for application in linear viscoelasticity are presented. They are obtained from the entropy inequality in a weak form. Moreover, integration by parts, an expansion formula, approximation formula and generalized variational principles of Hamilton's type are given. Hamilton's action integral in the first principle, do not coincide with the lower bound in the fractional integral, while in the second principle the minimization is performed with respect to a function from a specified space and the order of fractional derivative.