摘要
一般的整数阶发展方程存在周期解,然而由于分数阶微积分具有记忆和遗传特征,分数阶发展方程几乎不存在周期解.首先运用Laplace变换论证含有Caputo分数阶导数的Cauchy问题周期解的不存在性.然后应用压缩映射原理证明非线性发展方程存在唯一的渐近周期解.
There are periodic solutions for general integer-order evolution equations.However,because of the memory and genetic characteristics of fractional calculus,there are almost no periodic solutions for fractional-order evolution equations.Firstly,Laplace transformation is used to prove the nonexistence of periodic solutions for Cauchy problems with Caputo fractional derivatives.Then,the contractive mapping principle is applied to prove that there exists a unique asymptotic periodic solution for nonlinear evolution equations.
作者
南杰措
卓义峰
NAN Jiecuo;ZHUO Yifeng(School of Mathematics and Computer Science,Northwest University for Nationalities,Lanzhou Gansu 730000)
出处
《宁夏师范学院学报》
2019年第4期5-13,共9页
Journal of Ningxia Normal University
基金
国家自然科学基金项目(61463046)
中央高校基本科研业务费项目(31920180022)
甘肃省自然科学基金项目(17JR5RA279)
关键词
分数阶微分方程
周期解
渐近周期解
存在性
Fractional differential equation
Periodic solution
Asymptotically periodic solution
Existence