I am unfortunately rather uneducated in electronics,
So you are best not to do this project, it could be fatal.
The arduino like any other board would be capable of controlling this sort of thing but you can not generate these signals directly because you can only get 5V directly from most micro controllers.
This sort of thing requires high voltages and you generate these with external circuits that turn the DC into AC, then step up the AC voltage using a transformer or inductor and then convert it back to DC.
Your software controls this system and any programming error might result in a voltage overdoes for your victim.