Solveis finding the correct solution to a logical problem after analysis. It implies that you understood the problem, and deal with it successfully. It is used for something that is not easy without taking complicated measures or thinking process.
Fixis making a physical changeto something, is used for something that takes concrete procedures. Although you can fix something, you may not understand the problem, you may just did something and the problem went away. You fixed it, but you don’t understand why.
You can fix a car, but you can't fix a mystery or a math problem.
If there is a body or concrete things that are broken, you fixit. You never solveit. You sometimes hear people say, "Can you fix me (up)?", but you don't hear "Can you solve me?"
Resolvemeans the end of a conflict or a problem. When you resolve something (a problem, an issue), you have completed it, it is done. Although it is done, it doesn’t mean you dealt with it correctly. Resolve only means you had concluded it with one way (of many possible choices).
"The issue has been resolved, although none of us is happy with the outcome."
Resolvetypically concerns emotional problems.
"Resolve a dispute."