一类非线性分数阶微分方程正解的存在性

Existence of positive solutions for a class of nonlinear fractional differential equations

研究了一类带有积分边界条件的非线性两项分数阶微分方程正解的存在性.该文考虑以下两项分数阶微分方程{-D_(0+)^(α)u(t)+au(t)=f(t,u(t)),0<t<1,u(0)=u′(0)=0,u(1)=μ∫_(0)^(1)u(r)dr,其中2<α<3,a>0,μ>0,D_(0+)^(α)是标准的Riemann-Liouville导数,非线性项f(t,x)在t=0,1和x=0可能是奇异的.运用锥上的不动点定理得出以上方程正解的存在性结果.

The existence of the positive solutions of nonlinear two-term fractional differential equations is considered.The fractional differential equation {-D_(0+)^(α)u(t)+au(t)=f(t,u(t)),0<t<1,u(0)=u′(0)=0,u(1)=μ∫_(0)^(1)u(r)dr ,is considered,where 2<α<3,a>0,μ>0,and D_(0+)^(α) is the standard Riemann-Liouville derivative,the nonlinearity f(t,x)may be singular at both t=0,1 and x=0.The existence results of positive solutions of the above equations are obtained using the fixed point theorem on cone.