一类分数阶Euler-Bernoulli梁耦合格点系统解的存在唯一性  

Existence and Uniqueness of Solutions of a Class of Fractional Order Euler-Bernoulli Beam Coupling Lattice Systems

作　　者：景蓓 魏毅强[1] 

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2016年第5期456-460,469,共6页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金面上项目(11472184)

摘　　要：在Euler-Bernoulli梁格点系统中,考虑了热效应影响,并且将其推广到分数阶形式,研究了一类分数阶Euler-Bernoulli梁耦合格点系统解的存在唯一性.其中,运用连续紧映射原理和Schauder’s不动点定理,证明了该梁耦合格点系统解的存在性,运用压缩映射原理,证明了该梁耦合格点系统解的唯一性.该结果对工程中一些关于Euler-Bernoulli梁模型的梁的弹性振动问题的讨论和估算有一定的指导意义.An exploration was made on existence and uniqueness of the solutions of a class of fractional order Euler-Bernoulli beam coupling lattice systems,which was effected by the thermal effect and generalized to the fractional order form.By using the principle of continuous maps and Schauder＇s fixed point theorem,the existence of solutions of the lattice system was obtained.And by using the contraction mapping theory,uniqueness of solution of the lattice system was proved.In the engineering,the result has guiding significance for the discussion and estimation of elastic vibration of beam about Euler-Bernoulli beam model.

关 键 词：分数阶格点系统 CAPUTO导数 巴拿赫压缩映射原理 存在唯一性 

分 类 号：O175[理学—数学]