Banach空间分数阶微分方程边值问题解的存在性与唯一性

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

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{-D——0~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],Dα0+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.

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 E,{-Dα0＋u（t）=f（t,u（t））,t∈I,u（0）=u′（0）=u′（1）=θis considered,where 2〈α≤3 is a real number,I=[0,1],Dα0＋is the standard Riemann-Liouville fractional derivative,f：I×E→Eis continuous,θis 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.