Is electric voltage fade in and fade out?
Everything has capacitance so you cannot instantly turn an LED (or anything) on or off.  There is always some time required to discharge that capacitance.  For a normal (non-white) LED, turning on/off takes tens or hundreds of nanoseconds during which time the brightness gradually increases or decreases towards the final value.
In the case of a white LED, the phosphor coating remains excited for microseconds after the diode stops emitting.  During this time even though the LED is off, the phosphor continues to glow.