河北师范大学学报—

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刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
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Banach空间分数阶微分方程边值问题解的存在性与唯一性

甘肃农业大学理学院, 甘肃兰州 730070
DOI： 10.13763/j.cnki.jhebnu.nse.2018.05.002

The Existence and Uniqueness of Solutions for Boundary Value Problems of Fractional Differential Equations in Banach Spaces

CHEN Yanli, LI Hong, SONG Weixin, ZHANG Feng

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摘要/Abstract

摘要：

应用单调迭代技巧研究了抽象的Banach空间E中一类非线性分数阶微分方程边值问题
{-D₀^α+u（t）=f（t，u（t）），t∈I，
u（0）=u'（0）=u'（1）=θ
解的存在性，其中2<α≤3是实数，I=[0，1]，D₀^α+是标准的Riemann-Liouville导数，f：I×E→E连续，θ为E中的零元.在较弱的单调性条件和非紧性测度条件下，通过构造上下解的单调迭代过程，获得该边值问题最小、最大解对的存在性及解的存在唯一性.

Abstract：

By the monotone iterative technique, the existence of solution for the boundary value problems of the fractional differential equation in an abstract ordered Banach space
{-D₀^α+u(t)=f(t,u(t)),t∈I,
u(0)=u'(0)=u'(1)=θ
is considered, where 2<α ≤ 3 is a real number,I=[0,1],D₀^α+ is the standard Riemann-Liouville fractional derivative,f:I×E→E is continuous, θ is the zero element of E. Under more general conditions of monotonicity and noncompactness measure,the existence of the minimum and maximum solutions are derived and the existence and uniqueness of solution for the boundary value problem are obtained by using the mono tone iteration scheme with upper and lower solution.

关键词

关键词： 分数阶微分方程 ; 上下解方法 ; 单调迭代技巧 ; 非紧性测度 ; 边值问题

Key words： fractional differential equations ; the method of upper and lower solutions ; monotone iterative technique ; measure of noncompactness ; boundary value problem

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