Muslims say that Jesus did not die on the cross. Is there any historical evidences to their (Muslims)claims?
First of all, the fact that Muhammad claimed Jesus did not die or was not resurrected has a problem up front. Muhammad lived nearly six hundred years after Christ. How would he know anything that was not known previously? What possible reason would there be to trust Muhammad’s opinion on whether Jesus was killed or was raised from the dead? He did not know anyone who knew Jesus. He had relatively little contact with Christians and, as far as I know, had no access whatsoever to historical materials that would be relevant to the question of whether Jesus was raised from the dead. So, the fact that Muslims claim Jesus was not killed or raised from the dead tells me literally nothing whatsoever about whether he was or was not resurrected.
Getting to your question, the simple answer is a definite no. There is no evidence, either that Jesus was not killed or that he did not raise from the dead. To be honest, it is somewhat unfair to ask for evidence that Jesus was not killed or raised. What would the evidence be? A body? Record of him living after his crucifixion (other than the forty days or so before his ascension)? Obviously not. Contemporaries who said he was not raised? That is a possibility. There is no direct evidence of people from people at that time who denied the resurrection, but I am sure there were people who did not believe Jesus was raised from the dead.
It is hard to prove a negative, and therefore, the fact that there is no evidence that Jesus was not raised is not a very good evidence that he was. Really, a much better question than the one you asked is whether there is evidence he was raised from the dead. In that case, the answer is a definite yes. Here are three historical facts: 1. Jesus was crucified, under the authority of Pontius Pilate. 2. The resurrection of Jesus was claimed publicly in Jerusalem in the immediate aftermath of the event. 3. The tomb where Jesus’ body was placed was empty.
The first fact is established by the non-Christian authors as well as believers. Josephus, Tacitus and the authors of the Jewish Talmud, as well as several Christian authors all agree with fact #1. Historians, including skeptics and honest atheists all agree on fact number 2. There is no way to explain the creation and growth of the Christian church unless it is true. Fact #3 is established because of fact #2. If Jesus’ body had been in the tomb, then belief in the resurrection could never have taken hold in Jerusalem in the immediate aftermath.
These facts all, plus the more than 500 eyewitnesses to the resurrection (1 Corinthians 15:1-6) all strongly support that Jesus was indeed raised from the dead. Add to that the fact that there is no evidence he did not raise and you have a pretty strong case.
This is a major problem for Islam because the Qur’an clearly says that Jesus was not resurrected. If he was, then the Qur’an is not inspired by God and Islam is in big trouble. This is why Muslims claim that the New Testament was corrupted. The problem with this is that, like with their claims that Jesus was not resurrected, there is NO EVIDENCE of New Testament corruption on a scale which would allow that the crucifixion accounts were added as corruptions. Honestly, can anyone thinking rationally claim that the resurrection accounts in all four gospels were added much later than the gospels were written? This proposal is really ridiculous. The reason this is particularly problematic for Muslims is that Muhammad himself said in the Qur’an that the gospels (called the Injil in the Qur’an) in their original forms were inspired. There is literally no possible way for Muslims to support that the Qur’an is inspired unless the crucifixion accounts were added after the gospels were written, yet no serious person can believe this. That is why you have found Muslims trying to claim that there is evidence that Jesus was not raised from the dead, and that the Bible is corrupted.