The basic question after reading your post that comes in mind is, "What company is offering fractional mining?", and I ask this because so far, I have never seen either an individual or a company offering to let you pay a portion of a mining equipment's price and maintenance to get a share of the profits made from it and the reason for not offering such a thing is obvious: it's not profitable enough to allow the company to get some profit itself and then share it with others as well.
Due to the difficulty, mining with a single equipment is not possible anymore because it will barely get to mine anything since the competition between companies and firms mining Bitcoin is pretty high which increases the difficulty, so for you to be able to mine Bitcoin, you need to set up more than one equipment so that you can have more hash power. So, considering that and the electricity cost and other maintenance costs, it's not possible for a company to allow you to pay only a portion of a single equipment's buying and maintenance cost and get profit from it.