非线性Caputo型分数阶微分方程耦合系统边值问题解的存在性和唯一性

Existence and Uniqueness of Solutions of the Boundary Value Problem for a Coupled System of Nonlinear Caputo Fractional Differential Equations

研究了一类带有积分边界条件非线性Caputo型分数阶微分方程耦合系统{~cD~αu(t)+f(t,ν(t))=0,0<t<1,~cD~βν(t)+g(t,u(t))=0,0<t<1,u(0)=u′(0)=…=u^((n-2))(0)=u^((n))(0)=0,u(1)=λ∫01u(s)ds,ν(0)=ν′(0)=…=ν(n-2)(0)=ν(n)(0)=0,ν(1)=λ∫01v(s)ds解的存在性和唯一性问题.利用Schauder不动点定理和Banach压缩映射原理,得到了该耦合系统解的存在性和唯一性的充分条件,并举例说明定理的有效性.

In this paper, we studied the existence and uniqueness of positive solutions for a class of Caputo fractional differential coupled system with integral boundary value conditions below.The existence and uniqueness of positive solutions were obtained by applying the Schauder fixed-point the- orem and Banaeh contraction mapping principle, two examples were given to illustrate the advantages of our main results.