一致分数阶微分方程两点边值问题解的存在性

Existence of solutions for the two-point boundary value problem of a conformable fractional differential equation

本文运用Leray-Schauder非线性择抉理论和Leray-Schauder度理论得到了一致分数阶微分方程两点边值问题{D^(b)(D^(a)+λ)u(t)=f(t,u(t)),0<t<1,u(0)=0,D^(a)u(1)=0解的存在性,其中α,β∈(0,1],λ是实数,Dα,Dβ是一致分数阶导数,u(t)∈E=C([0,1],R),f(t,u(t)):[0,1]×R→R是给定的连续函数.最后本文给出一个例子作为应用.

In this paper,by using the Leray-Schauder’s nonlinear alternative theory and Leray-Schauder degree theory,we obtain the existence of solutions for the following two-point boundary value problem of conformable fractional differential equation:{D^(b)(D^(a)+λ)u(t)=f(t,u(t)),0<t<1,u(0)=0,D^(a)u(1)=0 whereα,β∈(0,1],λis a real number,Dα,Dβare conformable fractional derivatives,u∈E=([0,1],R),f(t,u(t)):[0,1]×R→R is a continuous function.An example is given to verify the results.