Hi,
You can call the .m or functions from app designer same as how we generally do it in Editor.
Additionally, you can take inputs through the app, send them as arguments to your functions and get the output back to the app designer and display them.
Fore more information, refer to the following documentation page: https://www.mathworks.com/help/matlab/app-designer.html?s_tid=CRUX_lftnav