Help with MOSFET buck converter
To open the gate you need Vgs more than the threshold voltage. For instance 5V. But in your circuit you will not get it. 

You need boost capacitor and a diode to power up the NPN, and actually you need something like optocoupler instead it, so Arduino would be able to drive it. 

And you need a diode between ground and inductor left terminal. 

I recommend you to google any TI DC/DC and see how they work. Start with TPS54160.