To better explain how star fragments work you must wish on a wishing star when its nighttime. Just tilt the left analog stick down to look up at the sky and when you hear a twinkle sound then Press A to wish on a star. The more wishes you do the more star fragments you do. You will have to wait the next day and when you do go around your beach and you should see star fragments showing up. Its a slow process since there could be more during the day. Whatever you do DO NOT time travel backwards because it can mess up the process. You can time travel forward, but don't go backwards.
You will find them on the beach!! <3 Also if this is your 2nd+ meteor shower in a week I do not think they let you get anymore fragments. I think its a max of 20 per meteor shower per week.