含有积分、反周期和带P-Laplacian算子的分数阶微分方程边值问题解的存在性  

Existence of Solutions for Boundary Value Problems of Fractional Differential Equations with Integral,Anti-periodic and P-Laplacian Operators

作　　者：胡芳芳 胡卫敏 HU Fang-fang;HU Wei-min(College of Mathematics and Statistics,Yili Normal University,Yining 835000,China)

机构地区：[1]伊犁师范大学数学与统计分院,新疆伊宁835000

出　　处：《数学的实践与认识》2021年第4期207-216,共10页Mathematics in Practice and Theory

基　　金：新疆维吾尔自治区自然科学基金(2019D01C331)。

摘　　要：利用格林函数的性质和Banach压缩映射原理讨论了含P-Laplacian算子反周期边值问题的解.首先,求出与该边值问题相关的格林函数并给出了格林函数的性质;然后将边值问题转化为与其等价的积分方程,利用格林函数的性质及Banach压缩映射原理得到边值问题解的唯一性;最后给出实例验证结果的合理性.Using the properties of the Green’s function and the principle of Banach contraction mapping,we prove the existence of solutions to the anti-periodic boundary value problem of a class of Caputo fractional differential equations with the P-Laplacian operator.First,according to the fractional differential equations and the boundary conditions of integral and antiperiodic,the Green’s function related to the boundary value problem is obtained,and the properties of the Green’s function are studied;Then,the boundary value problem transformed into the equivalent integral equation by applying the Green function,we obtain the existence result of the solution of the boundary value problem;Finally,two corresponding examples are given to verify the rationality of the result.

关 键 词：Caputo分数阶微分 积分和反周期 P-LAPLACIAN算子 BANACH压缩映射原理 

分 类 号：O175.8[理学—数学]