| 基于Ph,e下Riemann-Liouville分数阶微分方程解的存在唯一性 |
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| 引用本文： | 刘宏伟,张玲玲.基于Ph,e下Riemann-Liouville分数阶微分方程解的存在唯一性[J].数学的实践与认识,2021(2):232-240. |
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| 作者姓名： | 刘宏伟 张玲玲 |
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| 作者单位： | 太原学院应用数学系;太原理工大学数学学院 |
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| 基金项目： | 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)。 |
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| 摘 要： | 利用基于集合Ph,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Ph,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.
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| 关 键 词： | 分数阶微分方程 不动点 存在唯一性 锥理论 集合Ph e |
Existence and Uniqueness of Solutions for a Class of Riemann-Liouville Fractional Differential Equation based on set Ph,e |
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| LIU Hong-wei,ZHANG Ling-ling.Existence and Uniqueness of Solutions for a Class of Riemann-Liouville Fractional Differential Equation based on set Ph,e[J].Mathematics in Practice and Theory,2021(2):232-240. |
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| Authors: | LIU Hong-wei ZHANG Ling-ling |
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| Institution: | (Department of Mathematics,Taiyuan University,Taiyuan 030001,China;College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China) |
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| Abstract: | Based on a class of mixed monotone fixed point theorems on the set Ph,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 Ph,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. |
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| Keywords: | fractional differential equations fixed point existence and uniqueness cone theory set Ph e |
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