时间分数卡普托导数与一般化的福克-普朗克和一般化的朗格文方程中的其他整分演算子对比
Qing Wei1,2, Wei Wang2, Hongwei Zhou3
1School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing 100083, People's Republic of China.
本研究对异常扩散模型的各种分数导数运算符进行了比较. 符合性和卡普托-朗格温方程对缩放和分数布朗运动有希望,与指数或米塔格-莱弗勒核不同.
科学领域:
- 物理 物理学 物理
- 复杂的系统复杂的系统.
- 数学建模的数学建模
背景情况:
- 分数扩散和福克-普朗克方程模型复杂系统中的异常扩散.
- 这些模型经常使用卡普托或里曼-利乌维尔分数导数,与米塔格-莱弗勒放松相关.
- 新的运算符如卡普托-法布里齐奥,Atangana-Baleanu和符合衍生品已经出现.
研究的目的:
- 用各种分数导数运算符分析广义化的福克-普朗克和朗格文方程.
- 将这些概括方程所描述的动态与已建立的模型进行比较.
- 为物理相关的异常扩散场景确定合适的运营商.
主要方法:
- 分析时刻,时间平均平均平方位移和自动 covariance 函数.
- 研究包含不同整微分演算子的广义朗格温方程.
- 从一般化模型与缩放布朗运动和分数布朗运动进行动态的比较.
主要成果:
- 带有指数和米塔格-莱弗勒核的整微分量运算符不适合在相关的扩散场景中用于福克-普朗克和朗格文方程.
- 符合的朗格温方程表现出类似于缩放的布朗运动的动态.
- 卡普托·兰格温方程表现出类似于分数布朗运动的属性.
结论:
- 分数导数运算符的选择显著影响异常扩散模型的动态.
- 符合性和卡普托运算符为模拟特定类型的异常扩散提供了可行的替代方案.
- 已建立的模型,如缩放和分数布朗运动,可以通过特定的泛用朗格温方程有效地表示.
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