I am not aware of the concept of "quantum mathematical fractional topology" as a well-established field or concept in quantum computing or mathematics. However, it's important to note that the field of quantum computing is rapidly evolving, and new concepts and ideas are constantly being explored.
Topology is a branch of mathematics that studies properties of space that are preserved under continuous transformations, such as stretching, bending, and twisting. Fractional topology, on the other hand, typically refers to topological concepts involving fractional dimensions or fractional transformations.
While there has been significant research and development in applying topological concepts to quantum computing, such as topological quantum computing, where the topological properties of certain states are utilized to perform quantum computations, the specific notion of "quantum mathematical fractional topology" is not a widely recognized term in the field.
It's possible that you may be referring to a more specific concept or a newer development that has emerged since I'm not interested in that topic as much as i used to and my answer might be a bit outdated. If you could provide more context or clarify the specific area or concept you are referring to, I may be able to offer more targeted information.