Which Functions are Fractionally Differentiable

IF 0.7 3区 数学 Q2 MATHEMATICS
G. Vainikko
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引用次数: 43

Abstract

s of MMA2015, May 26–29, 2015, Sigulda, Latvia c © 2015 WHICH FUNCTIONS ARE FRACTIONALLY DIFFERENTIABLE? G. VAINIKKO Institute of Mathematics, University of Tartu Liivi 2, Tartu 50409, Estonia E-mail: gennadi.vainikko@ut.ee We define a fractional differentiation operator as the inverse to Riemann-Liouville integral operator, and examine the relations of this most natural concept with more popular fractional differentiation operators of Riemann-Liouville and Caputo. Our main result concerns the description of the range of Riemann-Liouville integral operator in the space of continuous functions. As the result we can describe, in particular, the class of functions that are differentiable in the sense of Riemann-Liouville and Caputo. Also the Abel equation with coefficient function of two variables can be examined on the basis of Riemann-Liouville’s operator inversion.
哪些函数是分数可微的
5 of MMA2015, May 26-29, Sigulda, Latvia c©2015哪些函数是分数可微的?我们将分数阶微分算子定义为Riemann-Liouville积分算子的逆算子,并研究了这个最自然的概念与更流行的Riemann-Liouville和Caputo分数阶微分算子的关系。我们的主要结果是关于连续函数空间中Riemann-Liouville积分算子的值域的描述。因此,我们可以特别地描述一类在黎曼-刘维尔和卡普托意义上可微的函数。在Riemann-Liouville算子反演的基础上,还可以检验具有两个变量的系数函数的Abel方程。
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来源期刊
CiteScore
1.80
自引率
0.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.
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