Riemann-Liouville分数阶微分方程边值问题的积分形式解  

Integral Solutions to Boundary Value Problems of Riemann-Liouville Fractional Differential Equations

作　　者：史新杰 汪文帅 龙品红 SHI Xinjie;WANG Wenshuai;LONG Pinhong(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China;Ningxia Basic Science Research Center of Mathematics,Yinchuan 750021,China)

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021 [2]宁夏数学基础学科研究中心,宁夏银川750021

出　　处：《宁夏大学学报(自然科学版中英文)》2025年第1期7-15,共9页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(42064004,12161067);宁夏科技领军人才项目(2022GKLRLX04)。

摘　　要：研究了一类Riemann-Liouville分数阶微分方程Robin边值问题解的存在唯一性,并以积分形式给出了边值问题的解.在该Robin边值问题满足特定条件时,证明了解的存在唯一性,然后通过几个Riemann-Liouville分数阶微分方程边值问题数值解的算例说明结论的有效性.In this paper,the existence and uniqueness of solutions to a class of Robin boundary value problems for Riemann-Liouville fractional differential equations are studied,which are presented in integral form.For these problems,the existence and uniqueness of solutions can be proved under certain conditions.Furthermore,some examples of numerical solutions to boundary value problems for Riemann-Liouville fractional differential equations are provided to illustrate the validity of our conclusions.

关 键 词：积分解 分数阶微分方程 边值问题 

分 类 号：O175.8[理学—数学]