Which Functions are Fractionally Differentiable?

被引：66

作者：

Vainikko, Gennadi ^{[1
,2
]}

机构：

[1] Univ Tartu, Inst Math & Stat, J Liivi 2, EE-50409 Tartu, Estonia

[2] Estonian Acad Sci, Kohtu 6, EE-10130 Tallinn, Estonia

来源：

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2016年 / 35卷 / 04期

关键词：

Inversion of Riemann-Liouville operator; Riemann-Liouville fractional derivative; Caputo fractional derivative; description of fractionally differentiable functions;

D O I：

10.4171/ZAA/1574

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We examine the existence of fractional derivatives of a function in terms of the pointwise convergence or equiconvergence of certain improper integrals containing this function. The fractional differentiation operator is treated as the inverse to the Riemann-Liouville integral operator. Technically, we give a description of the range of the Riemann-Liouville operator. The results are reformulated also for Riemann-Liouville and Caputo fractional derivatives.

引用

页码：465 / 487

页数：23

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