具非局部条件的非线性分数阶微分方程耦合系统的正解  

Positive solutions for coupled system of nonlinear fractional differential equations with nonlocal conditions

作　　者：齐超凡 薛春艳[1] QI Chaofan;XUE Chunyan(School of Applied Science, Beijing Information Science & Technology University, Beijing 100192, China)

机构地区：[1]北京信息科技大学理学院,北京100192

出　　处：《沈阳师范大学学报（自然科学版）》2021年第4期375-379,共5页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11471146)。

摘　　要：对一类具有黎曼-刘维尔导数的非线性分数阶微分方程耦合系统进行研究,得到其正解的存在性。此类耦合系统具有积分边界条件且带有参数。首先,运用分数阶微积分的定义,将此分数阶微分方程耦合系统转化为一个与之等价的常微分方程耦合系统;其次,在Banach空间中定义一个新的具有矢量的锥,同时构造一个全连续算子;最后,通过运用Precup的一个新的不动点定理具有矢量的Krasnoselskii锥不动点定理,得到算子的不动点,进而得到分数阶微分方程耦合系统正解的存在性,再拓展使用此定理,得到耦合系统正解的局限性和多重性。In this work,we study the existence of positive solutions for a class of a coupled system of nonlinear fractional differential equations with Riemann-Liouville derivatives.This kind of coupled system has integral boundary conditions and parameters.Firstly,the coupled system with fractional-order differential equations is transformed into an equivalent coupled system of ordinary differential equations by the definition of fractional-order calculus.Secondly,a new cone with a vector is defined in Banach space,and a fully continuous operator is constructed.Finally,by using Radu Precup,a new fixed point theorem with vector Krasnosellskii fixed point theorem,the fixed point of this operator is obtained,and then the existence of positive solutions for the coupled system of fractional differential equations is obtained.The limitation and multiplicity of the positive solutions of the coupled system are obtained by further extending the theorem.

关 键 词：分数阶微分方程系统 黎曼-刘维尔导数 Krasnoselskii锥不动点定理 局限性和多重性 正解 

分 类 号：O175.14[理学—数学]