一类非线性分数阶微分方程解的存在性

EXISTENCE OF SOLUTIONS FOR A CLASS NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

利用经典的Leray-Schauder择一定理和Banach压缩映射原理给出了分数阶微分方程Dρu(t)=f(t,u(t),Dβu(t))的初值问题解的存在惟一性.

The existence and uniqueness of the solutions for a class nonlinear factional differential equation Dρu（t）=f（t,u（t）,Dβu（t）） is discussed by making use of the Leray-Schauder nonlinear alternative theorem and Banach contraction mapping principle.