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.
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