Abstract
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.
Highlights
1 Introduction In recent years, more experiments and theories show that many abnormal phenomena that occur in engineering and applied sciences can be described by fractional calculus, and fractional differential equations have been proved to be valuable tools in various science fields, such as physics, biological engineering, mechanics, artificial intelligence, chemistry engineering, etc
K = 1, 2, . . . m, By employing a fixed point theorem of φ-concave-convex mixed monotone operator, existence and uniqueness of positive solutions to the initial value problem were obtained
In our work, the nonlinear term is mixed monotone, so by means of the fixed point theorem of φ-concave-convex mixed monotone operator, we can show the existence and uniqueness of positive solution
Summary
More experiments and theories show that many abnormal phenomena that occur in engineering and applied sciences can be described by fractional calculus, and fractional differential equations have been proved to be valuable tools in various science fields, such as physics, biological engineering, mechanics, artificial intelligence, chemistry engineering, etc. (see [1,2,3,4,5]). M, By employing a fixed point theorem of φ-concave-convex mixed monotone operator, existence and uniqueness of positive solutions to the initial value problem were obtained. The authors investigated the control problem of positive solutions and proved the existence-stability of an optimal control.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
