分数阶脉冲微分方程反周期边值问题解的存在性

Existence of Solution for Impulsive Anti-periodic Boundary Value Problem of Fractional Differential Equation

研究了一类具有Caputo分数导数的分数阶脉冲微分方程反周期边值问题解的存在性与唯一性.首先,运用分析的方法计算出边值问题的Green函数,并讨论了Green函数的性质;其次,将微分方程边值问题转化为积分算子方程,利用不动点理论及压缩映射原理,得到了关于反周期边值问题解的存在性及唯一性的多个新结论.特别地,研究的边值问题在脉冲条件和边界条件中都涉及状态变量的分数阶导数.

The existence and uniqueness of solutions were studied for anti-periodic boundary value problem of impulsive fractional differential equation with Caputo fractional derivative.The Green＇s function of the boundary value problem was calculated by means of the analysis method and the properties of the Green＇ s function were also discussed.The boundary value problem of fractional differential equation was then transformed into an integral operator equation,and by using fixed point theorem and contraction mapping principle,some new results for the existence and uniqueness of the anti-periodic solution for boundary value problem were obtained.In particular,it can be seen the fractional derivative of state variables is involved in both the impulse and boundary conditions of the boundary value problem discussed.