throught a capacitor and a resistance.
In series with the input? That's not right... The input will "float" to an undefined value. And then your signal will ride on top of that floating input.
Since you are not reading 0-255 you should use the [u]map()[/u] function.
And look at the [u]Smoothing Example[/u]. That's a moving average. You'll want to slow it down. The example has a 1ms delay (it's updated 1000 times per second). For a "fade" you'll probably want to update around 10 times per second or less and you may want more elements in your array, etc.
float RED_VALUE = 25; //Define the initial value for red colour
It's not only your "initial value", you never change it.
And it doesn't need to be a float.
analogWrite(LED_GREEN_PIN, (GREEN_VALUE / 255) * Level_Value);
I think I know what you're trying to do, but since GREEN-VALUE is always 255... that doesn't do much...
There is also no timing/delay so you're not going to see a "fade".
You're also not constraining Level_Value to 255 or less. I've never tried it, but I assume analogWrite() "rolls-over" if you exceed 255. That is, if you write 256 you'll have zeros in the 8 least-significant bits so you'll probably be writing zero.