非线性分数阶微分方程奇异边值问题的唯一解

Unique Solution for the Singular Boundary Value Problem of A Nonlinear Fractional Differential Equation

研究了非线性分数阶微分方程边值问题Dα0+u(t)+f(t,u(t))=0,0<t<1;u(0)=u(1)=u'(0)=0,的Green函数及其性质,其中2<α≤3是实数,Dα0+是标准Riemann-Liouville型微分,并利用锥不动点定理和混合单调方法证明了奇异边值问题解的唯一性。最后举例加以说明。

Green＇s function and its properties for the nonlinear fractional differential equation boundary valueproblem Dο^α＋μ（t）＋f（t,μ（t））=0,0〈t〈1;μ（0）=μ（1）=μ＇（0）=0, is considered where2〈α〈3 is a real number, and Dο^α is the standard Riemann-Liouville differentiation. As an application of Green＇s function and its properties, uniqueness of solution is given for the singular boundary value problem by means of a fixed-point theorem on cones and a mixed monotone method. One concrete example is respectively given to explain the above theorem finally.