Preheat an air fryer to 320 degrees F (180 degrees C). Line the air fryer basket with aluminum foil.
Mix sultanas and brown sugar together in a bowl.
Place a puff pastry sheet on a clean work surface. Put an apple on the pastry and fill the core with the sultana mixture. Fold the pastry around the apple so that it is fully covered. Repeat with remaining pastry, apple, and filling.
Place dumplings into the prepared basket and brush with melted butter.
Set timer for 25 minutes; cook dumplings until golden brown and the apples are soft.