According to my understanding an induction burner doesn’t cook with fire rather with magnetic energy (whatever that really means)
I know when it comes to cooking on Shabbos “Bishul bechama” is allowed, one can potentially argue that this is even further away from “derech bishul” then bishul bechama being the sun is a type of heat source and this isn’t (to my understanding) so perhaps this could in theory be allowed on Shabbos? obviously a bad idea to actually allow it, and clearly chazal would’ve prohibited it’s use on Shabbos similar to “toldah dechama”
When it comes to bishul Akum would it be allowed?
The magnetic energy that is used, is only a different way to heat up the pot, after that the pot cooks the food the same way it cooks the food when on a gas burner. Regarding shabbos cooking with an induction burner is not considered bishul b’chama, because it is becoming a common thing to cook this way. This would be similar to what R’ Moshe Feinstein zt”l wrote (Igros Moshe O:CH 3-52) regarding cooking in a microwave, that since it will become a normally used medium of cooking it isn’t considered bishul bchama. Regarding bishul akum, although it can be argued that it is not cooking with an actual fire, nevertheless the kashrus agencies (OU, COR, MK), regard it as regular cooking because indeed the food is cooked, and comes out the same as regular cooking.
Otzar halachos Bishul Akum 2-12 in Biurim.