Newton's second law usually is written:
$$F(t,x,\dot{x})=m\ddot{x}$$
Why not to allow forces which depend on higher derivatives? Is there any principle hidden?
Is it the same reason why lagrangians of higher order aren't considered? I mean, usually it is said that you can give up higher derivatives redefining variables...Does it include non-local forces with infinite number of derivatives?
In summary, is there any physical principle why forces which depend on higher derivatives, or even negative order or fractional order derivatives are not included in the common physical expositions and formulations of classical mechanics and newton's laws?