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分数阶微积分是一个古老而又新颖的课题,近30年来,由于在包括分形现象在内的物理、工程等诸多应用学科领域应用的拓展,激发了科研人员对分数阶微积分的巨大热情。分数阶微分方程现在已应用于分数物理学、混沌与湍流、粘弹性力学与非牛顿流体力学、高分子材料的解链、自动控制理论、化学物理、随机过程和反常扩散等许多科学领域。分数阶微分方程边值问题是非线性常微分方程理论研究中一个活跃而成果丰硕的领域。本文讨论了分数阶微分方程边值问题的一些理论,介绍了作者的著作《分数阶微分方程边值问题理论及应用》的基本内容。
Abstract：Fractional order calculus is an ancient and also a new topic.For nearly 30 years,it has inspired researchers enormous enthusiasm of fractional order calculus due to the great application development many fields such as physics,engineering,fractal phenomenon,etc.Fractional order differential equations is now applied to physics,chaos and turbulence,viscoelastic mechanics and non-Newtonian fluid mechanics,solution of polymer chain,automatic control theory,chemical physics,stochastic process,abnormal diffusion and other many scientific fields.Fractional differential equation boundary value problem of the nonlinear ordinary differential equation is an active and fruitful field.This paper discusses some theories of the fractional differential equation boundary value problems,and introduces the basic content of the author's book " Theory and application for the fractional differential equation boundary value problems".
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基本信息:
中图分类号:O175.8
引用信息:
[1]白占兵.分数阶微分方程边值问题研究简介[J].数学建模及其应用,2017,6(02):1-10.
基金信息:
国家自然科学基金(11571207)