一致分数阶时滞微分方程边值问题解的存在性与唯一性  

Existence and Uniqueness of Solutions for Boundary Value Problems of Conformable Fractional Delay Differential Equations

作　　者：张敏 周文学[1] 黎文博 ZHANG Min;ZHOU Wenxue;LI Wenbo(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《吉林大学学报（理学版）》2023年第5期1007-1013,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11961039,11801243);兰州交通大学校青年科学基金(批准号:2017012).

摘　　要：用Leray-Schauder度理论和Banach压缩映射原理研究一致分数阶时滞微分方程边值问题{D^(β)_(0)+u(t)=f(t,u(t-τ)),t∈[0,1],u(t)=φ(t),t∈[-τ,0],u(0)+u′(0)=0,u(1)+u′(1)=0解的存在性与唯一性.在非线性项满足增长性条件和Lipschitz条件下,分别得到了该边值问题解的存在性与唯一性结果,并举例说明所得结果的适用性.By using Leray-Schauder degree theory and Banach contraction mapping principle,we studied the existence and uniqueness of solutions for boundary value problems of conformable fractional delay differential equations {D^(β)_(0)+u(t)=f(t,u(t-τ)),t∈[0,1],u(t)=φ(t),t∈[-τ,0],u(0)+u′(0)=0,u(1)+u′(1)=0,when the nonlinear term satisfied the growth condition and the Lipschitz condition,we obtained the results of existence and uniqueness of solution for the boundary value problem respectively,and gave an example to illustrate the applicability of the obtained results.

关 键 词：一致分数阶导数 时滞 边值问题 LERAY-SCHAUDER度理论 BANACH压缩映射原理 

分 类 号：O175.8[理学—数学]