含有参数的分数阶微分方程在集合Ph,e中解的存在唯一性
Existence and Uniqueness of Solutions to Fractional Differential Equations with Parameters in Set Ph,e
摘要: 本文研究了一类含有参数的算子不动点定理，得到了不动点的存在唯一性以及该不动点关于参数的单调性与连续性。以此为基础研究了一类含有参数的分数阶微分方程多点边值问题，最终得到了方程解的存在唯一性和该唯一解关于参数的单调性、连续性。最后举例说明了结果的可行性。
Abstract: This paper investigates a class of fixed point theorems with parameter operators, obtaining the existence and uniqueness of fixed points as well as the monotonicity and continuity of the fixed points with respect to the parameters. Building upon this, it explores a class of multi-point boundary value problems for fractional differential equations with parameters, ultimately obtaining the existence and uniqueness of solutions to the equations, along with the monotonicity and continuity of the unique solution with respect to the parameters. Finally, examples are provided to illustrate the feasibility of the results.
文章引用：陈孝虎, 张玲玲, 王慧. 含有参数的分数阶微分方程在集合Ph,e中解的存在唯一性[J]. 应用数学进展, 2024, 13(4): 1853-1861. https://doi.org/10.12677/aam.2024.134174

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