Cannot infer type arguments for ArrayAdapter<>

Sometimes the methods do not run directly in the activity and do not have access to it, not because of this, but because of the getApplicationContext ()

    ArrayAdapter adapter = new ArrayAdapter<>(getApplicationContext(), android.R.layout.simple_list_item_1, mutableBookings);

Try using type in your Adapter declaring. You are missing the type of your mutableBookings:

final ArrayAdapter adapter = new ArrayAdapter<String>(this, android.R.layout.simple_list_item_1, mutableBookings);

You need to pass a Context to the Constructor of ArrayAdapter. You're actually in initializing it in a Fragment class, so this is not valid as a Context. Try calling

final ArrayAdapter adapter = new ArrayAdapter<String>(getActivity(), 
                                android.R.layout.simple_list_item_1,
                                mutableBookings);