状态依赖脉冲Caputo分数阶微分方程解的存在唯一性

Existence and Uniqueness of Solutions for State DependentImpulsive Caputo Fractional Differential Equations

针对状态依赖脉冲Caputo分数阶微分方程,利用不动点方法研究方程解的存在唯一性;首先,定义一个全连续算子,利用Schaefer不动点定理及Gronwall不等式讨论对应的非脉冲方程解的存在性结论;然后利用状态依赖脉冲函数项的单调条件及解的延拓方法得到每个脉冲区间上状态依赖脉冲Caputo分数阶微分方程局部解及整体解的存在性结论;最后利用压缩映射原理得到状态依赖脉冲Caputo分数阶微分方程整体解的唯一性,改进了已有的结果。

For the state dependent impulsive Caputo fractional differential equation,the fixed point method is used to study the existence and uniqueness of the solution.Firstly,we define a completely continuous operator,and discuss the existence of solutions of the corresponding nonimpulsive Caputo fractional equations by using Schaefer fixed point theorem and Gronwall inequality.Secondly,we obtain the existence of local and global solutions of state dependent impulsive Caputo fractional differential equations on each impulsive interval by using the monotone condition of state dependent impulsive function term and the extension method of solutions.Finally,by using the compression mapping principle,the uniqueness of the global solution of the state dependent impulsive Caputo fractional differential equation is obtained,which improve the existing results.