向量值分数阶时滞微分方程的适定性 献给余家荣教授100华诞

Well-posedness of vector-valued fractional differential equations with delay

本文利用向量值Holder连续函数空间C^α(R;X)上的算子值Fourier乘子定理,给出实轴上向量值分数阶时滞微分方程D^βu(t)=Au(t)+Fut+f (t), t∈R具有C^α-适定性的充分条件,其中A为某Banach空间X上的线性闭算子, F为从C([-r, 0];X)到X的有界线性算子, r> 0固定,函数u的t平移ut定义为ut(s)=u(t+s)(t∈R, s∈[-r, 0]),β> 0固定, D^βu为函数u的β-阶Caputo导数.

By using operator-valued C^α-Fourier multiplier results on vector-valued H?lder continuous function spaces C~α(R;X), we obtain a necessary and sufficient condition of the C~α-well-posedness for the following fractional equations with finite delay:D^βu(t) = Au(t) + Fut + f(t), t ∈ R,where A is a closed linear operator on a Banach space X, F is a bounded linear operator from C([-r, 0];X) to X for some fixed r > 0, ut is defined by ut(s) = u(t + s) for t ∈ R, s ∈ [-r, 0], β > 0 is fixed and D~β u is the fractional derivative of u in the sense of Caputo.