Gary Cottrell continues his series on the authorship of the Gospels.
Here is the conclusion on his observations on Luke and Acts:
So, I must leave you with an uncertain conclusion. I do tend to accept the traditional authorship of Luke and Acts as being written by Luke, the companion of Paul. Dating is a difficult subject, and I am not able to offer a conclusion that satisfies even me. The ending of Acts seems to point to a date before Paul’s death; however, that requires a date too early to fit into the chronology of the gospels as we know it. Two possibilities present themselves. One is that Luke and Acts were written later in the first century which allows Luke to make use of Mark’s gospel. The other possibility is that our accepted chronology of the gospels is wrong. Either Mark was written even earlier than AD 60, or (and this is unlikely) Luke was written before Mark.
I am afraid I must leave us with questions for which there are at this time no good answers. At the same time, I still see no compelling reason to deny that Luke and Acts were written by Luke, the companion of Paul. I have read no convincing arguments to contradict that, and it still appears to be the simplest explanation.