| 一类带有偏差量的任意分数阶非线性微分方程边值问题唯一正解的存在性 |
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| 引用本文： | 段永红,王文霞.一类带有偏差量的任意分数阶非线性微分方程边值问题唯一正解的存在性[J].华中师范大学学报(自然科学版),2022,56(4):567-572. |
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| 作者姓名： | 段永红 王文霞 |
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| 作者单位： | (1.太原学院数学系， 太原 030032； 2.太原师范学院数学系， 山西 晋中 030619) |
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| 摘 要： | 该文研究了一类带有偏差量的任意分数阶非线性微分方程边值问题正解的存在唯一性，利用锥理论及混合单调算子和算子不动点定理获得了该边值问题存在唯一正解的充分条件，并给出了一个具体的例子以显示理论结果.
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| 关 键 词： | 边值问题 Riemann-Liouville分数阶导数 正解 锥 |
| 收稿时间： | 2022-08-15 |
The existence and uniqueness of positive solutions for a class of boundary value problems of arbitrary fractional order differential equations with deviated arguments |
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| DUAN Yonghong,WANG Wenxia.The existence and uniqueness of positive solutions for a class of boundary value problems of arbitrary fractional order differential equations with deviated arguments[J].Journal of Central China Normal University(Natural Sciences),2022,56(4):567-572. |
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| Authors: | DUAN Yonghong WANG Wenxia |
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| Institution: | (1.Department of Mathematics， Taiyuan College， Taiyuan 030032， China；2.Department of Mathematics， Taiyuan Normal University， Jinzhong， Shanxi 030619， China) |
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| Abstract: | In this paper， the existence and uniqueness of positive solutions for a class of boundary value problems of arbitrary fractional order nonlinear differential equations with deviated arguments is studied. By using the cone theory and the fixed point theorem for the sum of mixed monotone operators， sufficient conditions for existence of the unique positive solution for the boundary value problems are obtained. An example is given to illustrate theoretical results. |
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| Keywords: | boundary value problem Riemann-Liouville fractional derivative positive solution cone |
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