中文摘要：

该文目的在于给出如下分数阶微分方程解的存在唯一性结论D^αx（t）=f（t,x（t））,t∈J：=（0,1],0〈α〈1, lim t^（1-α）x（t）=x（1）,其中f在t=0可以是奇异的.主要的工具是上下解方法、最大值原理和单调迭代技术.最后举例说明所获结论的应用。

英文摘要：

The purpose of this paper is to give some sufficient conditions for the existence and uniqueness of solutions to the fractional differential equation as follows{D^αx（t）=f（t,x（t））,t∈J：=（0,1],0〈α〈1, lim t^（1-α）x（t）=x（1）, where D-α denotes the Riemann-Liouville fractional derivative,f may be singular at t = 0.Lower and upper solutions method,maximum principle together with iterative technique are employed.An example is presented to illustrate the application of results obtained.