一类新的非线性分数阶微分方程多点边值问题的唯一解
Unique Solutions for a New Class of Multi-Point Boundary Value Problem of Nonlinear Fractional Differential Equations
DOI: 10.12677/AAM.2020.99182, PDF,    科研立项经费支持
作者: 邢高峰：太原理工大学数学学院，山西 太原；张玲玲*：太原理工大学数学学院，山西 太原；北京理工大学爆炸科学与技术国家重点实验室，北京
关键词: 分数阶微分方程；混合单调算子；存在唯一性；Fractional Differential Equations； The Mixed Monotone Operator； Existence and Uniqueness
摘要: 本文研究了一类新的高阶分数阶微分方程多点边值问题。首先，我们计算得到了G(t,s)，同时构造了所研究问题的算子方程，然后利用新集合Ph,e中的混合单调算子不动点定理及G(t,s)的性质，得出了此类方程解的存在唯一性。最后，给出一个例子证明方法的有效性。
Abstract: In this paper, we study a new class of higher-order fractional differential equations with multi-point boundary value problems. First, we obtain G(t,s) through calculation, and construct the operator equation of the problem under study. Then, using the fixed point theorem of the mixed monotone operator in the new set Ph,e and the properties of G(t,s), the uniqueness of the solution of this type of equation is obtained. Finally, an example is given to illustrate the effectiveness and feasibility.
文章引用：邢高峰, 张玲玲. 一类新的非线性分数阶微分方程多点边值问题的唯一解[J]. 应用数学进展, 2020, 9(9): 1546-1555. https://doi.org/10.12677/AAM.2020.99182

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