Approximate controllability and optimal controls of fractional evolution systems in abstract spaces

Advances in Difference Equations

Jianwei Liu¹  Haiyong Qin¹  Xin Zuo¹  Lishan Liu² 

[1] Department of Automation, China University of Petroleum (Beijing), Changping, China;School of Mathematical Sciences, Qufu Normal University, Qufu, China

关键词: fractional evolution systems;    approximate controllability;    optimal controls;    semigroup theory;    fixed point theorem;   

DOI  :  10.1186/1687-1847-2014-322

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, under the assumption that the corresponding linear system is approximately controllable, we obtain the approximate controllability of semilinear fractional evolution systems in Hilbert spaces. The approximate controllability results are proved by means of the Hölder inequality, the Banach contraction mapping principle, and the Schauder fixed point theorem. We also discuss the existence of optimal controls for semilinear fractional controlled systems. Finally, an example is also given to illustrate the applications of the main results. MSC:26A33, 49J15, 49K27, 93B05, 93C25.

【 授权许可】

CC BY