Author:
Qin Haiyong,Liu Jianwei,Zuo Xin,Liu Lishan
Abstract
Abstract
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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference27 articles.
1. Podlubny I: Fractional Differential Equations. Academic Press, San Diego; 1999.
2. Miller KS, Ross B: A Introduction to Fractional Calculus and Differential Equations. Wiley, New York; 1993.
3. Lakshmikantham V, Leela S, Vasundhara Devi J: Theory of Fractional Dynamic Systems. Cambridge Scientific Publishers, Cambridge; 2009.
4. Trasov VE: Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. Springer, New York; 2010.
5. Diethelm K Lecture Notes in Mathematics. In The Analysis of Fractional Differential Equations. Springer, New York; 2010.
Cited by
9 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献