Optimal control of nonlocal fractional evolution equations in the α -norm of order \((1,2)\)

Advances in Difference Equations

article

Niazi, Azmat Ullah Khan¹  Iqbal, Naveed³  Mohammed, Wael W.³ 

[1] Faculty of Mathematics and Computational Science, Xiangtan University;Department of Mathematics and Statistics, University of Lahore;Department of Mathematics, Faculty of Science, University of Ha’il;Department of Mathematics, Faculty of Science, Mansoura University

关键词: Fractional evolution equations;    α -Mild solutions;    Existence;    Continuous dependence;    Optimal control;   

DOI  :  10.1186/s13662-021-03312-0

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This paper investigates the optimal control for a class of nonlocal fractional evolution equations of order$\gamma \in (1,2)$ in Banach spaces. An adequate definition of α-mild solutions is obtained and the existence, uniqueness and continuous dependence of α-mild solutions for the presented control system are also established. The existence of optimal pairs of nonlocal fractional evolution systems is also demonstrated with a view on the construction of the Lagrange problem. Finally, an example is propounded for the presentation of optimal control.

【 授权许可】

CC BY