Existence-uniqueness of positive solutions to nonlinear impulsive fractional differential systems and optimal control

Boundary value problems

Nan Zhang¹  Bibo Zhou²  Lingling Zhang³  Shu Song⁴ 

[1] College of Mathematics, Taiyuan University of Technology, Yingze West Road, 030024, Taiyuan, P.R. China;College of Mathematics, Taiyuan University of Technology, Yingze West Road, 030024, Taiyuan, P.R. China;Department of Mathematics, Lvliang University, 033000, Lvliang, P.R. China;College of Mathematics, Taiyuan University of Technology, Yingze West Road, 030024, Taiyuan, P.R. China;State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, 100081, Beijing, P.R. China;Shanxi Engineering Vocational College, Xinjian Road, 030009, Taiyuan, P.R. China;

关键词: φ;    Fractional differential equation;    Impulsive terms;    Optimal control;   

DOI  :  10.1186/s13661-020-01461-x

来源: Springer

【 摘 要 】

In this thesis, we investigate a kind of impulsive fractional order differential systems involving control terms. By using a class of φ-concave-convex mixed monotone operator fixed point theorem, we obtain a theorem on the existence and uniqueness of positive solutions for the impulsive fractional differential equation, and the optimal control problem of positive solutions is also studied. As applications, an example is offered to illustrate our main results.

【 授权许可】

CC BY