分数阶微分方程初值问题解的存在性  

The Existence of Solutions to Initial Value Problem for Fractional Differential Equation

作　　者：崔亚琼 康淑瑰 陈慧琴 CUI Ya-qiong;KANG Shu-gui;CHEN Hui-qin(School of Mathematics and Statistics,Shanxi Datong University,Datong Shanxi,037009)

机构地区：[1]山西大同大学数学与统计学院,山西大同037009

出　　处：《山西大同大学学报（自然科学版）》2023年第5期37-40,共4页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：国家自然科学基金项目[11871314];大同市基金项目[2020147]。

摘　　要：利用Banach不动点定理和Schauder’s不动点定理,研究非线性分数阶微分方程初值问题解的存在性,其中分数是小于1的正数,初始点是零点,低一阶分数导数在初始点的值是非零常数。鉴于该初值问题等价的积分方程含有奇异项的在零点无界,通过选择恰当的完备空间,在非线性项满足合适的条件下,利用上述两个不动点定理,分别得到该初值问题唯一解和至少一个非平凡解的存在性。Using Banach fixed point theorem and Schauder's fixed point theorem,this paper studies the existence of solutions to the initial value problem of nonlinear fractional differential equations,where the fraction is a positive number less than 1,the initial point is zero,and the value of the lower first-order fractional derivative at zero point is a non-zero constant.Since the equivalent integral equation of the initial value problem contains singular terms that are unbounded at zero point,by choosing an appropriate complete space,if nonlinear terms satisfy some appropriate conditions,by applying the above two fixed point theorems,we obtain the existence of the unique solution and at least one nontrivial solution to the initial value problem,respectively.

关 键 词：分数阶微分方程 初值问题 BANACH不动点定理 Schauder’s不动点定理 解 

分 类 号：O175.14[理学—数学]