Welcome to the board! I hope you'll have fun here

I would advise a band called Train mostly. Not the same style, but their newest album has some similarities with Jovi, at least to me.

My Chemical Romance, Daughtry or All American Rejects are bands that have Bon Jovi as one of their inspirations, but none of them are really trying to write music similar to Jovi, just a few similar things that you wouldn't notice if you don't know about it (however, I kinda like MCR for a lot same reasons I love Jovi). McFly comes to my mind as well.

If you had prefered the 80s Jovi, I would've easily advised Journey, Aldo Nova and, obviously, Def Leppard, but as I see that's not the case.

I hope my post slightly helps you. It's nice to see a younger fan who actually likes the band's newer stuff as opposed to 80s or 90s. I really wish I could say that about myself as my favorite era is the one with the least amount of studio albums, LOL