Yes. Solid rocket fuel contains its own oxidizer.
The rocket carries its own supply of oxygen with which to burn the fuel.
If its fuel has an oxidizer (oxygen-producing solid fuel) in it like solid rocket fuel, then yes.
A rocket motor (rocket engine) does not need air from the atmosphere. It carries the oxidant (source of oxygen) as well as the fuel.
liquid fuel
There are solid rocket fuels, and there are liquid rocket fuels.
The name of a common rocket fuel is liquid hydrogen, which is often used in combination with liquid oxygen. There are also other types of rocket fuels including solid fuels and hybrid fuels, but liquid hydrogen is one of the most commonly used.
There are choice of solid liquid and gas fuel propellant. For space discovery rocket it is usually use liquefied hydrogen and oxygen as fuel. Missile and ICBM use solid propellant for long storage time. Choice is depend on the type and need.
Modern model rocket fuel is a solid fuel.
Solid rocket fuel.
Solid fuel
Rocket fuel is either liquid or solid. Other kinds are being developed.
in the engine