中文摘要：

该文研究一类非线性分数阶微分方程边值问题D^αu（t）＋f（t,u（t））=0,0〈t〈1,u（0）=u（1）=0的可解性，其中1〈d≤2是实数，D^α是适型分数阶导数，f：[0，1]×[0，∞）→[0，∞）是连续函数．研究的难点之一是相应的Green函数G（t，s）在s=0处是奇异的．利用逼近法和锥上的不动点定理，得到了正解的存在性和多解性．

英文摘要：

In this paper, we establish the solvability of a class nonlinear fractional differential equation boundary value problem D^αu（t）＋f（t,u（t））=0,0〈t〈1,u（0）=u（1）=0,where 1 〈 α ≤ 2 is a real number, [0, 1] x [0, ∞） → [0,∞） is a continuous Green＇s function G（t, s） is singular at theorems on cone, some existence and D- is the conformable fractional derivative, and f ： function. One of the difficulty here is the corresponding s = 0. By the use of approach method and fixed-point multiplicity results of positive solutions are acquired.