非光滑热曲线的分数阶次可微性研究  

Fractional differentiability of the non-smooth heat curve

作　　者：吴国成[1] 石祥超[1] 

机构地区：[1]四川大学水利水电学院,土木工程博士后流动站,成都610065

出　　处：《物理学报》2012年第19期33-36,共4页Acta Physica Sinica

基　　金：国家自然科学基金重点项目(批准号:51134018);四川省青年科技基金(批准号:2012JQ0031);水力学与山区河流开发保护国家重点实验室开放基金(批准号:1112)资助的课题~~

摘　　要：自然界存在诸多的非光滑现象,如海岸线、岩石的裂隙和截面形貌等.经典的微积分理论和欧氏几何中的常用方法无法用来刻画其可微性.局部分数阶导数是局部化的分数阶导算子,是潜在的研究非光滑曲线微尺度性态的工具之一.本文首先回顾了基于分数阶积分和类Cantor集生成的阶梯曲线,然后利用一般的二项式展开,从分数阶可微函数的角度得到了非光滑热曲线的分数阶次可微性.There are many non-smooth objects in nature, such as coastline, rock fracture, cross section, whose differentiabilities cannot be described by ordinary calculus and methods in Euclidean geometry. The local fractional derivative is one of the potential tools to investigate the non-smooth problems. This study revisits the non-smooth curves generated from the fractional integrals and Cantor-like set. From the view of the fractional differentiable functions, the differentiabilities of the non-smooth curves are derived by using a binomial expansion.

关 键 词：分形 分数阶次可微性 不光滑曲线 全局行为 

分 类 号：O186[理学—数学]