Variational formulation and optimal control of fractional diffusion equations with Caputo derivatives

Advances in Difference Equations

Qing Tang¹  Qingxia Ma¹ 

[1] School of Mathematics and Physics, China University of Geosciences, Wuhan, China

关键词: fractional diffusion equation;    distributional weak Caputo derivative;    fractional Sobolev space;    37L05;    47J30;   

DOI  :  10.1186/s13662-015-0593-5

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY