Existence and optimal controls for nonlocal fractional evolution equations of order (1,2) in Banach spaces

Advances in Difference Equations

article

Pang, Denghao¹  Jiang, Wei²  Niazi, Azmat Ullah Khan³  Sheng, Jiale² 

[1] School of Internet, Anhui University;School of Mathematical Sciences, Anhui University;Faculty of Mathematics and Computational Science, Xiangtan University;Department of Mathematics and Statistics, University of Lahore

关键词: Fractional evolution equations;    Mild solution;    Existence;    Continuous dependence;    Optimal control;   

DOI  :  10.1186/s13662-021-03430-9

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we mainly investigate the existence, continuous dependence, and the optimal control for nonlocal fractional differential evolution equations of order (1,2) in Banach spaces. We define a competent definition of a mild solution. On this basis, we verify the well-posedness of the mild solution. Meanwhile, with a construction of Lagrange problem, we elaborate the existence of optimal pairs of the fractional evolution systems. The main tools are the fractional calculus, cosine family, multivalued analysis, measure of noncompactness method, and fixed point theorem. Finally, an example is propounded to illustrate the validity of our main results.

【 授权许可】

CC BY