To add to @Ben Thuls's answer, you may track page splits using extended events and thus track fragmentation indirectly. Check this awesome article by Paul Randal to familiarize yourself with the LOP_DELETE_SPLIT log operation and then create a session which will look like that:
CREATE EVENT SESSION [Page Splits] ON SERVER
ADD EVENT sqlserver.transaction_log(SET collect_database_name = 1
WHERE (operation = $LOP_DELETE_ID$) ) --LOP_DELETE_SPLIT*
ADD TARGET package0.event_file(SET FILENAME = N'PageSplitsOutput.xel',MAX_FILE_SIZE = 200, MAX_ROLLOVER_FILES = 2, INCREMENT = 20)
WITH (MAX_MEMORY=4096 KB,EVENT_RETENTION_MODE=ALLOW_SINGLE_EVENT_LOSS,MAX_DISPATCH_LATENCY=30 SECONDS,MAX_EVENT_SIZE=0 KB,MEMORY_PARTITION_MODE=NONE,TRACK_CAUSALITY=OFF,STARTUP_STATE=OFF);
GO
And fill $LOP_DELETE_ID$
with the result from this:
SELECT *
FROM sys.dm_xe_map_values
WHERE name = 'log_op'
AND map_value = 'LOP_DELETE_SPLIT';