I don't believe there is any existing library that would do a straight conversion for you. There's a lot of libraries for displaying animated GIFs - far fewer native Objective-C libraries for creating them.
Fortunately, iOS does have support for saving as GIFs. There's an existing StackOverflow answer that covers how to create animated GIFs in-depth here:
Create and and export an animated gif via iOS?
...there's also a library on GitHub that abstracts the lower-level stuff away, although it's not been maintained for a while (link here).
All you'll need to do is create an array of the frames you want to convert into your GIF. I strongly recommend you don't try and convert every single frame in your 15 second video, if only because you'll end up with a very large GIF at a frame-rate that's too high. You would be better off picking every other, or even every 3/4 frames from your video sample. Capturing images from video is also pretty well documented on iOS.