You still need to do some more digging. It can be anything and slowness when "accessing the database" and checking the waits isn't going to tell you much.
The average wait time really isn't much - it's more the percentage of the waits. Those are hard to say as you would want a baseline to compare to. You can do a capture and then 24 hours later do another to get the waits for that 24 hour period. That would tell you more about the waits. The sqlskills site has an example of capturing for a time frame which you can modify to meet your needs.Capturing IO latencies for a period of time
If the slowness is just when they first access the database (users typically won't know when they are accessing just the application or accessing the database), you may want to consider looking at what is being executing from the application at the beginning of that process and look into tuning those queries/stored procedures, check the query stats, etc
You may still want to check sys.dm_io_virtual_file_stats to see if a particular file is being hit hard or indicates a lot of stalls.
You can also run an extended events session or server side trace to capture a login process from the application and see what is taking the most time.
I usually check statistics first instead of fragmentation - it often seems to be an issue when user report things becoming slower over time.