20、分数阶微分方程相关研究

分数阶微分方程相关研究

1. 脉冲分数阶微分方程

1.1 理论分析

在研究中，通过 (T (1,x0)(V )(t) = T(V )) 的等度连续性，可推出 (G(t, s)φ(s, co{T(V )(s), x0})、(ψco{T(V )(s), x0}) 和 (ϕco{T(V )(s), x0}) 是等度连续的。进而得到：
(\beta(T (2,x0)(V )(t)) = \beta(Tco{T (1,x0)(V )(t), x0}))
(\leq\parallel Mα\parallel\max(1, bζ1, bζ2)B(T(V ))\left(\frac{br}{\Gamma(r + 1)} + \frac{1}{b} (\frac{\mu}{\delta} + b)\right)\left(\frac{br}{\Gamma(r + 1)} + \frac{\mu}{\delta}\frac{br−1}{\Gamma(r)}\right))
( + mT\frac{br}{\Gamma(r + 1)} + mT(\frac{\mu}{\delta} + b) \frac{br−1}{\Gamma(r)} + mT\frac{br}{\Gamma(r + 1)} + mT^2 \frac{br−1}{\Gamma(r)})
(\leq\left(\parallel Mα\parallel\max(1, bζ1, bζ2) \frac{b∗}{\Gamma (r)}\left((m + 1)(\frac{\mu}{\delta})^2 + (3m + 2)\frac{\mu}{\delta} + 4m + 2\right)\right)^2\bet