非线性分数阶积分微分方程边值问题正解的存在性  

Existence of Positive Solutions for Boundary Value Problems of Nonlinear Fractional Integro-differential Equations

作　　者：杨晓莹 贾梅[1] 刘锡平[1] YANG Xiaoying;JIA Mei;LIU Xiping(College of Science,University of Shanghai for Science and Technology,Shanghai 200093)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《工程数学学报》2022年第6期925-940,共16页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11171220).

摘　　要：研究一类具有两个分数阶导数项的非线性分数阶积分微分方程积分边值问题。首先将原问题转化为只有一个导数项的等价形式,通过定义等价问题的上下解,再利用单调迭代技术建立了原问题正解的存在性与唯一性定理,给出了求其唯一正解的迭代格式和误差估计。最后给出实例说明所得结论的有效性和适用性。The integral boundary value problem for a class of nonlinear fractional integro-differential equations with two fractional derivative terms is studied.Firstly,the original prob-lem is transformed into an equivalent form with only one derivative term.The existence and uniqueness theorems of positive solutions of the original problem are established by defining the upper and lower solutions of the equivalent problem and using the monotone iterative tech-nique.The iterative schemes and error estimates for finding the unique solutions are obtained.Finally,an example is presented to illustrate the effectiveness and potential applications of our main results.

关 键 词：Riemann-Liouville分数阶导数 积分微分方程 边值问题 上下解 误差估计 

分 类 号：O175.8[理学—数学]