具有脉冲的半线性分数阶微分方程边值问题解的存在性

Existence of Solution to Boundary Value Problem of Semi-linear Fractional Differential Equations with Impulses

讨论下列脉冲分数阶微分方程边值问题解的存在性{~cD_(0^+)~qu(t)=λu(t)+f(t,u(t),(Ku)(t),(Hu)(t)),t∈J',1<q≤2,△u(t_k)=I_k(u(t_k)),△u'(t_k)=I_k~*(u(t_k)),t_k∈(0,T),k=1,...,m,Tu'(0)=-au(0)-bu(T),Tu'(T)=cu(0)+du(T),基于不动点定理,得到了边值问题解的存在性,并且给出例子.

Based on the fixed point theorem,the following boundary value problem for fractional differential equations with impulses is discussed to find the existence of solution to the problem and is exemplified.{~cD_(0^+)~qu(t)=λu(t)+f(t,u(t),(Ku)(t),(Hu)(t)),t∈J',1<q≤2,△u(t_k)=I_k(u(t_k)),△u'(t_k)=I_k~*(u(t_k)),t_k∈(0,T),k=1,...,m,Tu'(0)=-au(0)-bu(T),Tu'(T)=cu(0)+du(T),