一类分数阶微分方程边值问题的Lyapunov不等式

A Class of Boundary Value Problems for Fractional Differential Equations Lyapunov Inequality

对于一类分数阶微分方程边值问题,求解其相应的Lyapunov不等式.把分数阶微分方程转化为积分方程,结合边值条件,写出相应的格林函数.运用分析学技巧,研究格林函数的上下界.利用范数的定义和格林函数的上界,求解出Lyapunov不等式.作为应用,得到对应特征值问题中特征值的取值范围和一类Mittag-Leffler函数无实根的范围.

A Lyapunov inequality for boundary value problem for a class of nonlinear fractional differential equation is established.Firstly,a fractional differential equation is transferred into integral equation,and com bining with the boundary value conditions,the corresponding Green function is obtained.Then we use skills of analysis to study the upper and lower bounds of Green′s function.Finally,the Lyapunovinequality is solved by using the upper bounds of norm and Green′s function.As an application,we firstly get the range of eigenvalues for the corresponding eigenvalue problem; secondly,we obtain a rangewhere a class of Mittag-Leffler function has no real zero point.