The current position is that Ragnar's sons did indeed exist, but a historical Ragnar Fuzzypants probably didn't. In case you learned of him via Vikings, we have a section of the FAQ devoted specifically to the accuracy of Vikings. As for Ragnar Fuzzypants himself, we have a few more posts specifically on his historicity. I commend to your attention these:

• u/sagathain examines the man wearing fuzzy pants and his sons;
• u/y_sengaku looks at the man wearing fuzzy pants as a figure;
• and u/Platypuskeeper observes what we know of he who wears fuzzy pants.