一致分数阶微分方程两点边值问题解的存在性  

Existence of solutions for the two-point boundary value problem of a conformable fractional differential equation

作　　者：吴玉翠 周文学[1] 豆静 WU Yu-Cui;ZHOU Wen-Xue;DOU Jing(College 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：《四川大学学报（自然科学版）》2022年第1期24-28,共5页Journal of Sichuan University(Natural Science Edition)

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

摘　　要：本文运用Leray-Schauder非线性择抉理论和Leray-Schauder度理论得到了一致分数阶微分方程两点边值问题{D^(b)(D^(a)+λ)u(t)=f(t,u(t)),0<t<1,u(0)=0,D^(a)u(1)=0解的存在性,其中α,β∈(0,1],λ是实数,Dα,Dβ是一致分数阶导数,u(t)∈E=C([0,1],R),f(t,u(t)):[0,1]×R→R是给定的连续函数.最后本文给出一个例子作为应用.In this paper,by using the Leray-Schauder’s nonlinear alternative theory and Leray-Schauder degree theory,we obtain the existence of solutions for the following two-point boundary value problem of conformable fractional differential equation:{D^(b)(D^(a)+λ)u(t)=f(t,u(t)),0<t<1,u(0)=0,D^(a)u(1)=0 whereα,β∈(0,1],λis a real number,Dα,Dβare conformable fractional derivatives,u∈E=([0,1],R),f(t,u(t)):[0,1]×R→R is a continuous function.An example is given to verify the results.

关 键 词：一致分数阶微分方程 两点边值问题 Leray-Schauder非线性择抉理论 LERAY-SCHAUDER度理论 

分 类 号：O175.8[理学—数学]