局部分数阶微分系统的李雅普诺夫不等式研究
The Lyapunov-Type Inequality for Local Fractional Differential Equation

利用局部分数阶积分,将微分方程转换成积分方程,在此基础上构造格林函数,通过研究格林函数的最大值,得到李雅普诺夫不等式.此研究结果可分析局部分数阶微分系统解的不存在区间,也可研究局部分数阶微分系统特征值问题.
The local fractional differential equation with boundary conditions is studied,and a Lyapunov-type inequality is presented.The main steps are as follows,in the first place,the local fractional differential equation is transformed into the local integral equation through the local fractional integral tool.Green's function is established.Lyapunov-type inequality is obtained based on the simple analysis of the Green's function.The result can be applied to study the interval where the local fractional system has no nontrivial solution.In addition,eigenvalue for local fractional system can be studied through the result