一类ψ-Hilfer广义比例分数阶微分方程解的存在唯一性  

Existence and Uniqueness of Solutions for a Class of ψ-Hilfer Generalized Proportional Fractional Differential Equations

作　　者：李淑兰 胡卫敏 苏有慧[2] 贠永震 Li Shulan;Hu Weimin;Su Youhui;Yun Yongzhen(College of Mathematics and Statistic,Yili Normal University,Yining,Xinjiang 835000,China;School of Mathematics and Statistic,Xuzhou University of Technology,Xuzhou,Jiangsu 221018,China;Institute of Applied Mathematics,Yili Normal University,Yining,Xinjiang 835000,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]徐州工程学院数学与统计学院,江苏徐州221018 [3]伊犁师范大学应用数学研究所,新疆伊宁835000

出　　处：《伊犁师范大学学报(自然科学版)》2025年第1期1-10,共10页Journal of Yili Normal University(Natural Science Edition)

基　　金：新疆维吾尔自治区自然科学基金项目(2023D01C51);国家自然科学基金项目(12161079);伊犁师范大学科研创新团队培育计划项目(CXZK2021016);江苏省高等学校自然科学研究项目(22KJB110026);徐州市科技计划项目(KC23058)。

摘　　要：本文研究一类具有非局部边界条件的变阶ψ-Hilfer广义比例分数阶微分方程边值问题.首先,利用广义区间和分段常值函数的定义,将变阶ψ-Hilfer分数阶边值问题转化为等效标准常阶ψ-Hilfer分数阶边值问题;其次,运用Banach压缩映射原理和Schaefer's不动点定理得到边值问题解的存在唯一性;最后,构造一个实例来验证主要结果的合理性.This paper studies the boundary value problem of a class of variable order ψ-Hilfer generalized proportional fractional differential equations with nonlocal boundary conditions.Firstly,the variable order ψ-Hilfer fraction order boundary value problem is transformed into the equivalent standard constant order ψ-Hilfer fraction order boundary value problem by the definition of generalized interval and piecewise constant function.Secondly,the existence and uniqueness of the solution of the boundary value problem is obtained by using Banach contracting mapping principle and Schaefer's fixed point theorem.Finally,an example is constructed to verify the rationality of the main results.

关 键 词：广义比例分数阶导数 不动点定理 非局部边界条件 解的存在唯一性 

分 类 号：O175.8[理学—数学]