I worked two separate fellowships (which payed with a stipend, no W2) in two separate states this year. How do I report this? Do both state get to tax my income?

I worked one fellowship from Jan to Aug and received a monthly stipend (no W2).

Moved to a new state 

Started a new fellowship from Sept to Dec which payed in a stipend as well (no W2)

How do I enter this? Is the entire sum going to be taxed fully in both states? None of these payments where towards getting a degree.