The Existence of Positive Solution to a Nonlinear Fractional Differential Equation with Integral Boundary Conditions
The Existence of Positive Solution to a Nonlinear Fractional Differential Equation with Integral Boundary Conditions
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DOI：
10.1155/2011/546038
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发表时间：
2011-02
影响因子：
4.1
通讯作者：
M. Feng;Xiaofang Liu;H. Feng
中科院分区：
文献类型：
--
作者：
M. Feng;Xiaofang Liu;H. Feng
研究了一类带积分边界条件的非线性分数阶微分方程格林函数的表达式和性质，并利用锥上的不动点定理得到了正解存在性的一些结果。证明的基础是将问题归结为等价的第二类Fredholm型积分方程解。这些结果显著地推广和改进了许多已知结果，即使对于整数阶情况也是如此。
The expression and properties of Green's function for a class of nonlinear fractional differential equations with integral boundary conditions are studied and employed to obtain some results on the existence of positive solutions by using fixed point theorem in cones. The proofs are based on the reduction of the problem considered to the equivalent Fredholm integral equation of the second kind. The results significantly extend and improve many known results even for integer-order cases.