Dimmer effect (fade) on 12v LED using transistor and Arduino
You are using PNP transistors in a situation where NPN would be much more suitable. 

For that matter I would personally choose an N-channel MOSFET instead of BJT.







simulate this circuit &ndash; Schematic created using CircuitLab

R1 needs sizing for the current flow for your LED. R2 is used to keep the MOSFET turned off while the Arduino isn't actively driving the IO (it starts in INPUT mode while the bootloader runs for 2 seconds).

Make sure you choose a MOSFET that can a) handle the current you need, and b) is a logic level MOSFET with a \$V_{GS}\$ of no more than a couple of volts.