中文摘要：

应用不动点指数理论和Leray-Schauder度理论,主要讨论了非线性分数阶微分边值问题变号解的存在性。在非线性项满足合适的条件下,得到该边值问题至少存在一个正解,一个负解和一个变号解。特别地,若非线性项是奇的,则该边值问题至少存在一个正解,一个负解和二个变号解。

英文摘要：

Based on the fixed point index theory and Leray-Schauder degree theory,this paper mainly consider the existence of sign-changing solutions to nonlinear fractional differential boundary value problem.Under some suitable conditions on the nonlinearity,we obtain that this boundary value problem has at least one positive solution,one negative solution and one sign-changing solution.Especially,if the nonlinearity is odd,then the problem exists at least one positive solution,one negative solution and two sign-changing solutions.