Consider the Caldari Badger industrial. Its warp speed is 4.5 AU/sec. This means it travels at 675.000.000 km/sec, which is 2250c (rounded).
Consider a 15-jump trip, say from Jita system in The Forge to Colcer system in Everyshore.
This trip takes 6 minutes and 30 seconds in warp. Some leeway is applied for timing issues with starting/stopping the stopwatch. - The relativistic effects of the spool up time to warp are not considered. - The timer is stopped when the ship has reached the star gate at the far end of the system even though the warp drive is still active at that point (the ship was not on auto-pilot, it did not warp to zero, it was instructed to ‘jump’ on reaching the star gate at the far end of the system). - The relativistic effects of crossing the Einstein-Rosen bridge, the star gate, are not considered (even though the argument can be made that the transfer is not instantaneous point-to-point and the ship is crossing a divide of multiple light years, which very likely has profound effects).
In Einsteinian space this trip takes 390 seconds of time in warp. At 2250c, times 390, this trip takes 243.75 hours or 10.15 days in Newtonian space, one way. The results will obviously be different for other ship types moving slower or faster and depending on the distance traveled. It seems there are obvious implications with regards to contracts and manufacturing as well as the duration of conflict timers.
More importantly, and vastly more significant on a personal level, is that pilots will see their family and friends, relatives and associates, age rapidly the more time they spend in warp versus those people who do not travel at relativistic speeds.
Pilots spending a lot of time in fleet roams, insofar as they are not camping a gate, will see their time-spent-in-warp increase the more active their fleet operations are. The psychological effects on their lives as they are structured around classic human relationships deserves thoughtful and profound research and specialized care should be made available to all pilots so affected.