Existence of solutions to boundary value problem of a class of nonlinear fractional differential equations

被引：0
作者：
Yige Zhao
Yuzhen Wang
机构：
[1] Shandong University,School of Control Science and Engineering
来源：
Advances in Difference Equations | / 2014卷
关键词：
fractional differential equation; boundary value problem; fractional Green’s function; fixed point theorem;
D O I：
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学科分类号：
摘要：
In this paper, we study the existence of solutions for the boundary value problem of the following nonlinear fractional differential equation: D0+α[x(t)f(t,x(t))]+g(t,x(t))=0, 0<t<1, x(0)=x(1)=x′(0)=0, where 2<α≤3 is a real number and D0+α is the Riemann-Liouville fractional derivative. By a fixed point theorem in Banach algebra, an existence theorem for the boundary value problem of the above fractional differential equation is proved under both Lipschitz and Carathéodory conditions. Two examples are presented to illustrate the main results.
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