星图上非线性分数阶微分方程边值问题解的存在唯一性  

Existence and Uniqueness of Solutions for the Boundary Value Problems of Nonlinear Fractional Differential Equations on Star Graph

作　　者：韩晓玲 蔡蕙泽 杨虎军 Xiaoling Han;Huize Cai;Hujun Yang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070;Changqing College,Lanzhou University of Finance and Economics,Lanzhou 730022)

机构地区：[1]西北师范大学数学与统计学院,兰州730070 [2]兰州财经大学长青学院,兰州730022

出　　处：《数学物理学报（A辑）》2022年第1期139-156,共18页Acta Mathematica Scientia

基　　金：国家自然科学基金(12161079);甘肃省自然科学基金(20JR10RA086)。

摘　　要：该文运用Banach压缩映射原理和Schaefer不动点定理研究星图上的非线性分数阶微分方程边值问题{_(C)D^(α)_(0,x)u_(i)(x)=f_(i)(x,u_(i)(x),_(C)D^(β)_(0,x)u_(i)(x)),0<x<l_(i),i=1,2,…,k,u′_(i)(0)=u_(i)(1)=0,i=1,2,…,k,u″_(i)(l_(i))=k,u″_(j)(l_(j)),i,j=1,2,…,k,i≠j,k∑i=1u″_(i)(l_(i))=0,i=1,2,…,k,解的存在唯一性,其中2 <α≤3,0 <β<1,_(C)D^(α)_(0,x),_(C)D^(β)_(0,x)是Caputo分数阶导数,f_(i),i=1,2,…,k是[0,1]×R×R上关于三个变元连续可微的函数.In this paper,by using Banach’s contraction principle and Schaefer’s fixed point theorem,we study the existence and uniqueness of solutions for the boundary value problems of nonlinear fractional differential equations on star graph {_(C)D^(α)_(0,x)u_(i)(x)=f_(i)(x,u_(i)(x),_(C)D^(β)_(0,x)u_(i)(x)),0<x<l_(i),i=1,2,…,k,u′_(i)(0)=u_(i)(1)=0,i=1,2,…,k,u″_(i)(l_(i))=k,u″_(j)(l_(j)),i,j=1,2,…,k,i≠j,k∑i=1u″_(i)(l_(i))=0,i=1,2,…,k, where 2 <α≤3,0 <β<1,_(C)D^(α)_(0,x),_(C)D^(β)_(0,x) are Caputo fractional derivative,f_(i),i=1,2,…,k with respect to a continuously differentiable function of three variables on [0,1] × R × R.

关 键 词：分数阶微分方程边值问题 星图 BANACH压缩映射原理 Schaefer不动点定理 

分 类 号：O175.8[理学—数学]