In my research I need to show that the set

$$M := \{X \in \mathbb{R}^4,X≥0\}$$

where

$$X(t)=(x_1(t),x_2(t),x_3(t),x_4(t))^T$$

is positively invariant with respect the following system of fractional ordinary differential equation

$$D^{\alpha}(x(t))=f(t,x(t))$$

with initial non-negative condition $x(0)=x_0,$

where f is nonlinear and continuous.

My question is : how do I show that $M$ is positively invariant with respect to the system given ? Any ideas, references are appreciated.