一类分数阶微分方程边值问题正解的存在性

Existence of Positive Solutions for Boundary Value Problems with Fraction Differential Equation

研究了一类分数阶微分方程的边值问题:{Dα0+u(t)+f(u(t))=0,u(0)=0,u(1)=0,其中α(1<α<2)是实数,Dα0+是标准的Riemann-Liouville微分,f:[0,+∞)→[0,+∞)连续,t∈[0,1].利用范数形式的锥拉伸与锥压缩不动点定理,在满足适当的条件下,证明了该边值问题正解的存在性.

A class of fractional differential equation boundary value problem is studied. {D°0＋u（t）＋f（u（t））=0,u（0）=0,u（1）=0where a （ 1 （ a （ 2 ） is a real number, and D°0＋ is the standard Riemann-Liouville differentiation,t∈[0.1] t E E0,1-], and f：[O,＋00）→[0,＋00） is continuous. By using fixed-point theorem of cone expansion and compression of norm type, the existence of positive solutions for fraction differential equation boundary value problems is proved.