一类改进定义下的分数阶脉冲偏微分方程的振动性  

OSCILLATION OF MODIFIED RIEMANN-LIOUVILLE FRACTIONAL IMPULSIVE PARTIAL DIFFERENTIAL EQUATIONS

作　　者：徐伟杰 刘安平[1] 肖莉[1] XU Wei-jie;LIU An-ping;XIAO Li(School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China)

机构地区：[1]中国地质大学(武汉)数学与物理学院,湖北武汉430074

出　　处：《数学杂志》2020年第6期717-727,共11页Journal of Mathematics

基　　金：国家自然科学基金重点项目(41630643);国家自然科学基金青年项目(11801530).

摘　　要：本文研究了改进的Riemann-Liouville分数阶定义下的一类分数阶脉冲时滞偏微分方程在两类不同的边界条件下的强迫振动性质.利用分数阶微积分的性质、积分均值等方法,化分数阶偏微分方程为整数阶微分方程问题进行讨论,获得了一类方程解振动的充分条件.推广了一类分数阶脉冲偏微分方程解的振动性的结果.In this paper,we investigate the oscillation properties of a class of impulsive partial fractional differential equations with several delays subject to two different boundary conditions by using the properties of the modified Riemann-Liouville derivative.Some sufficient conditions for oscillation of the solutions are obtained by employing differential inequality method,and the results of a class of fractional impulsive partial differential equations were generalized in the paper.

关 键 词：改进的Riemann-Liouville分数阶定义 分数阶偏微分方程 脉冲 振动性 

分 类 号：O175[理学—数学]