文章基本信息

标题：Variational formulation and optimal control of fractional diffusion equations with Caputo derivatives
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作者：Qing Tang ; Qingxia Ma
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2015
卷号：2015
期号：1
页码：283
DOI：10.1186/s13662-015-0593-5
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper we start by giving a new definition of weak Caputo derivative in the sense of distributions, and we give a variational formulation to a fractional diffusion equation with Caputo derivative. We prove the existence and uniqueness of the solution to this weak formulation and use it to obtain a result on optimal control.
关键词：fractional diffusion equation ; distributional weak Caputo derivative ; fractional Sobolev space