Is there a source in halacha of mitzvah of kibud av by foster parents?
Essentially a foster child is not obligated in the mitzva of kibud av v’em, because the foster parents did not bore her. However the child is obligated to show them respect because of hakaras hatov because they brought him up and cared for him.
Shut Chasam Sofer O:CH 164, Igros Moshe Y:D 2-130, Gidulei Shmuel pg. 179.