非线性分数阶微分方程四点非局部边值问题
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非线性分数阶微分方程四点非局部边值问题
罗华;胡卫敏
【期刊名称】《绵阳师范学院学报》
【年(卷),期】2012(031)008
【摘要】From two to
three, and then to the infinite points, researches
of
BVPs( boundary value problems) of ODE (
ordinary differential equation)
were first
started in the initial stages of the calculus set
up by Newton
and Leibniz. These boundary value
problems of differential equations
are also
often referred to as non - local ordinary
differential equations
problems. In this
paper, the existence and uniqueness of solutions
'to a
four - point non - lo- cal boundary
value problems of nonlinear
differential
equations of fractional order q∈ (1,2) is
analyzed, with the
help of the Ascoli - Arzela
theorem, and the use of the uniqueness of
the
contracting mapping principle solution, followed
by Krasnoselskii
fixed point theorem for four
- point boundary value problem, is at least
one solution, and example is provided to
illustrate the theory.%从两点到
三点到m点再到无穷多点，对常微分方程边
值问题的研究最早始于牛顿和莱布
尼茨建立微积分的最初阶段。这些常微分方程多点边值问题也常常被称
为常微
分方程非局部问题。讨论阶数为q∈（1，2）的非线性分数阶微分方程四点非
局部边值
问题，借助Ascoli—Arzela定理，首先利用压缩映射原理得到解的唯
一性，其次利用Kra
snoselskii不动点定理得到四点边值问题至少存在一个解，
并且举例验证。