具有导数项的分数阶微分方程解的存在唯一性  

Existence and Uniqueness of Solutions of Fractional Differential Equations with Derivative Terms

作　　者：温世林 韩伟[1] 桑彦斌 WEN Shilin;HAN Wei;SANG Yanbin(School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,太原030051

出　　处：《重庆理工大学学报（自然科学）》2021年第1期258-263,共6页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(11571324);山西省高等学校科技创新项目(201802085);山西省1331重点创新团队、中北大学科研创新团队支持计划项目(TD201901)。

摘　　要：利用混合单调算子方程的不动点定理,结合格林函数以及锥上的不动点定理研究了一类具有导数项以及三点边界条件的非线性分数阶微分方程正解的存在唯一性。增加了导数项后的分数阶微分方程的难点在于对分数阶格林函数的计算及其范围的确定、对集合范数的定义以及它被赋予的半序关系。借助于格林函数的性质克服了该难点,扩展了已有文献的结果。By using the fixed point theorem of mixed monotone operator equations,combined with Green’s function and fixed point theorem on cone,the existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations with derivative term and three-point boundary condition are studied.The difficulty of the fractional differential equations after adding the derivative term lies in the calculation of the fractional-order Green’s function and its range determination,and the definition of the set norm and the semi-order relationship it is given.The difficulty is overcome by the nature of the Green’s function,and the results of the existing literature are expanded.

关 键 词：混合单调算子 φ(t)-凹凸算子 凹凸算子 不动点定理 分数阶微分方程 

分 类 号：O175.2[理学—基础数学]