Control LED strip with MOSFET and PWM Arduino
Your circuit won't work the way you imagine. 
You are trying to control the DC current flowing by changing the voltage across the LED strip (I assume that the strip has inbuilt resistors for the LEDs). 

While you could add extra capacitance across the gate of the FET and produce a changing Vg it will be quite difficult to control.

However if you select a PWM frequency well above any optical perception you can use the PWM to simply alter the period of time it is on compared to off. 

For example, if you set the PWM  frequency to say 490 Hz and have the PWM duty cycle at 50% ...then the LEDs will be about half brightness. You can then simply set the duty cycle to get the required brightness. 

The Arduino has a function (analogwrite()) which does this exactly. 

Read the analogwrite() documentation then follow any of the endless bouncing ball projects with a single LED to test it out. 

Since you are buffering the LED strip via an inverting amplifier (the FET) the values will be inverted for you, but you should be able to handle that.