Existence and uniqueness of solution for fractional differential equations with integral boundary conditions.
Existence and uniqueness of solution for fractional differential equations with integral boundary conditions.
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DOI：
10.14232/ejqtde.2009.1.69
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发表时间：
2009
影响因子：
1.1
通讯作者：
Xiping Liu;Mei Jia;Baofeng Wu
中科院分区：
文献类型：
--
作者：
Xiping Liu;Mei Jia;Baofeng Wu
Dx(t) + f(t, x(t), x(t)) = 0, t ∈ (0, 1), x(0) = ∫ 1 0 g0(s, x(s))ds, x(1) = ∫ 1 0 g1(s, x(s))ds, x(0) = 0, k = 2, 3, · · · , [α] − 1。利用Banach收缩映射原理，得到了关于存在唯一性的一些新结果。有趣的是，解的存在性和唯一性的充分条件取决于阶数 α。
Dx(t) + f(t, x(t), x(t)) = 0, t ∈ (0, 1), x(0) = ∫ 1 0 g0(s, x(s))ds, x(1) = ∫ 1 0 g1(s, x(s))ds, x(0) = 0, k = 2, 3, · · · , [α] − 1. By means of the Banach contraction mapping principle, some new results on the existence and uniqueness are obtained. It is interesting to note that the sufficient conditions for the existence and uniqueness of solutions are dependent on the order α.