基于P_(h,e)下Riemann-Liouville分数阶微分方程解的存在唯一性  

Existence and Uniqueness of Solutions for a Class of Riemann-Liouville Fractional Differential Equation based on set P_(h,e)

作　　者：刘宏伟 张玲玲 LIU Hong-wei;ZHANG Ling-ling(Department of Mathematics,Taiyuan University,Taiyuan 030001,China;College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原学院应用数学系,山西太原030001 [2]太原理工大学数学学院,山西太原030024

出　　处：《数学的实践与认识》2021年第2期232-240,共9页Mathematics in Practice and Theory

基　　金：爆炸科学与技术国家重点实验室(北京理工大学)开放基金(KFJJ19-06M);山西省归国留学人员科研基金(201903D421042);山西省教育科学“十三五”规划课题(ZX-18094,GH-19139)。

摘　　要：利用基于集合P_(h,e)上的一类混合单调算子不动点定理,研究了一类Riemann Liouville分数阶微分方程两点边值问题,获得了这类方程在集合P_(h,e)中解的存在性与唯一性,并用一组单调迭代序列逼近了该方程的唯一非平凡解.最后,利用一个实例验证了主要结论.Based on a class of mixed monotone fixed point theorems on the set P_(h,e),the twopoint boundary value problem of a class of Riemann-Liouville fractional differential equations is studied in this paper.The existence and uniqueness of the solution in the set P_(h,e) are obtained,and the unique nontrivial solution of the equation is approximated by a set of monotone iterative sequences.Finally,an example is used to verify the main conclusion.

关 键 词：分数阶微分方程 不动点 存在唯一性 锥理论 集合P_(h e) 

分 类 号：O175.8[理学—数学]