一类非线性共形分数阶微分方程的边值问题和脉冲初值问题  

Boundary Value and Initial Value Problems with Impulsive Terms for Nonlinear Conformable Fractional Differential Equations

作　　者：周碧波 张玲玲 白桑 ZHOU Bibo;ZHANG Lingling;BAI Sang(College of Biomedical Engineering,Taiyuan University of Technology,Taiyuan 030024,China;Department of Mathematics,Lvliang University,Lvliang 033000,China;State Key Laboratory of Explosion Science and Technology,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]太原理工大学生物医学工程学院,山西太原030024 [2]吕梁学院数学系,山西吕梁033000 [3]北京理工大学爆炸科学与技术国家重点实验室,北京100081

出　　处：《应用数学》2021年第1期47-58,共12页Mathematica Applicata

基　　金：Supported by the opening project of State Key Laboratory of Explosion Science and Technology(KFJJ19-06M);the Key R&D Program of Shanxi Province (201903D421042)。

摘　　要：本文研究一类非线性共形分数阶微分方程的边值问题和脉冲初值问题,利用基于锥理论的和型算子不动点定理和混合单调算子不动点定理,获得共形分数阶微分方程边值问题和脉冲初值问题正解的存在性和唯一性定理,并且得到一组可以逼近唯一正解的单调迭代序列,最后给出一个实例用来验证结论的有效性.In this paper,we are concerned with the existence and uniqueness of positive solutions for two kinds of nonlinear conformable fractional differential systems.By means of the fixed point theorems of sum-type operators and mixed monotone operators based on the cone theory,our results can not only guarantee the existence of a unique positive solution,but also be applied to construct an iterative scheme for approximating it.Finally,some examples are given to illustrate the main results.

关 键 词：存在唯一性 和型算子 混合单调算子 锥理论 脉冲 

分 类 号：O175.23[理学—数学] O175.26[理学—基础数学]