具左右分数阶导数的时滞微分方程的正解存在性及迭代求解法  

Existence and iteration for the delay differential equations involving left and right fractional derivatives

作　　者：魏春艳 刘锡平[1] WEI Chunyan;LIU Xiping(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2020年第5期417-423,共7页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11171220);上海理工大学教师教学发展研究项目(CFTD191006)。

摘　　要：研究了带有左右Riemann-Liouville分数阶导数的非线性时滞泛函微分方程积分边值问题。运用上下解方法,得到了边值问题正解的存在性和唯一性的新结论,给出了求边值问题近似解的迭代方法,并对近似解进行了误差估计。最后给出了具体实例用于说明本文所得结论与方法具有广泛的适用性。The integral boundary value problems of nonlinear delay functional differential equations with left and right Riemann-Liouville fractional derivatives were studied by using the method of lower and upper solutions.Some new results on the existence and uniqueness of solutions were established by using the method of upper and lower solutions,iteration method for solving differential equations and the error estimations were presented.Finally,an example was given out to illustrate the wide applicability of the results and methods.

关 键 词：左右分数阶导数 时滞 边值问题 正解 迭代方法 

分 类 号：O175.8[理学—数学]