Stepping up voltage from solar for a power brick (5V to 15V) possible?
You didn't provide enough details so I can't say for sure but it's possible to step up the voltage but it will not help you that you for a simple reason:

your device runs on 15-19 volts 2 amps which means it runs on 30-38 watts but the solar panels output is 28 watts , so if your power brick doesn't work on less than 2 amps or a voltage below 15 volts then it won't work again.