Fractional Ordinary Differential Equations

Abstract

First we consider simple fractional ordinary differential equations:

$$\displaystyle \begin{aligned} D_t^{\alpha} u(t) = -\lambda u(t) + f(t), \quad 0<t<T, {} \end{aligned} $$

(3.1)

$$\displaystyle \begin{aligned} d_t^{\alpha} u(t) = -\lambda u(t) + f(t), \quad 0 < t < T. {} \end{aligned} $$

(3.2)

We note that (3.1) and (3.2), etc. are considered pointwise.