Controllability of Hilfer fractional Langevin evolution equations

Frontiers in Applied Mathematics and Statistics

Applied Mathematics and Statistics

Junhua Ku¹  Haihua Wang² 

[1] College of Science, Qiongtai Normal University, Haikou, China;null;

关键词: control;    mild solution;    existence;    non-compactness;    evolution;   

DOI  :  10.3389/fams.2023.1191661

 received in 2023-03-22, accepted in 2023-04-14,  发布年份 2023

来源: Frontiers

【 摘 要 】

The existence of fractional evolution equations has attracted a growing interest in recent years. The mild solution of fractional evolution equations constructed by a probability density function was first introduced by El-Borai. Inspired by El-Borai, Zhou and Jiao gave a definition of mild solution for fractional evolution equations with Caputo fractional derivative. Exact controllability is one of the fundamental issues in control theory: under some admissible control input, a system can be steered from an arbitrary given initial state to an arbitrary desired final state. In this article, using the (α, β) resolvent operator and three different fixed point theorems, we discuss the control problem for a class of Hilfer fractional Langevin evolution equations. The exact controllability of Hilfer fractional Langevin systems is established. An example is also discussed to illustrate the results.

【 授权许可】

Unknown   
Copyright © 2023 Wang and Ku.