To move part of a fleet, you need to split it.
First you click on your desired fleet that have the ships you want to move.
On the fleet page, you will notice several tabs, click on Split.
You need to type the new fleet name, as by splitting you will divide your fleet in two.
Type the numbers next to each ship type you want, if you have 100 corvettes and want to move 10, inform the number.
The block on the right side will calculate how much marine and hangar space you will have on your new fleet, so you can split with those types to send it to where you want.
Are you done? Click the button