Apples are fussy about having their pollinators in teh same pollination group so your neighbour's trees may not be the best match. You can use Google to find the best pollinators for your tree.
Also, you need insects such as bees to do the pollination so make sure you have plenty of flowering plants nearbyto attract these insects to your garden.
Finally, this year there were heavy frosts just as the apples and pears round here were in full bloom. This damages the blossom and also deters insects from flying as it's too cold so may be another reason for lack of fruit set.