分数阶发展方程的周期解和渐近周期解

Periodic solutions and asymptotically periodic solutions for fractional evolution equations

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.