Banach空间一类非线性分数阶微分方程边值问题解的存在性  

The Existence of Solutions to a Boundary Value Problems of Nonlinear Fractional Differential Equations in Banach Spaces

作　　者：陈艳丽 宋卫信 黎虹 张锋 Chen Yan-li;Song Wei-xin;LI Hong;ZHANG Feng(Center for Quantitative Bioloby,College of Science,Gansu Agricultural University,Lanzhou,730070,Gansu,China)

机构地区：[1]甘肃农业大学理学院数量生物学研究中心,甘肃兰州730070

出　　处：《山西师范大学学报（自然科学版）》2018年第3期5-11,共7页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(31360104;41661022);草业生态系统教育部重点实验室暨甘肃省草学优势学科开放课题资助(2017-GSAU-CYJ-04;ZXYZK201702)

摘　　要：考虑Banach空间E中一类非线性分数阶微分方程边值问题{-Dα0+u(t)=f(t,u(t))t∈Iu(0)=u'(0)=u'(1)=θ解的存在性,其中2<σ≤3是实数,I=[0,1],Dα0+是标准的Riemann-Liouville导数,f:I×E→E连续,θ为E中的零元.用新的非紧性测度估计技巧,在f满足比较一般的增长条件和非紧性测度条件下,通过凝聚映射的不动点定理获得了该边值问题解的存在性.The existence of solution for the boundary value problems of the nonlinear fractional differential equation in an abstract Banach space E,{-Dα0＋u（ t） = f（ t,u（ t））t ∈ Iu（ 0） = u＇（ 0） = u＇（ 1） =θis considered,where 2 σ≤ 3 is a real number,I = [0,1],Dα0＋is the standard Riemann-Liouville fractional derivative,f： I × E→ E is continuous,θ is the zero element of E. Since a new estimation technique of noncompactness measure was introduced,under more general conditions of growth and noncompactness measure,the existence of solutions was obtained by using the fixed point theorem of condensing mappings.

关 键 词：非线性分数阶微分方程 凝聚映射 不动点定理 非紧性测度 边值问题 

分 类 号：O175.8[理学—数学]