'Fractional' is a concept where you own a share of a plane and that share gets you accesss to an entire fleet of aircraft, usually business jets or turboprops (there was an outfit that did it with Cirri, don't think they still exist).
What you are looking for is co-ownership or a partnership. AOPA has a website that tries to match folks interested in co-ownerships, the interface is clumsy and most of the people looking for shares seem quite unreasonable.
Go to the airport, put the word out that you are looking for a share. Pin up a flyer with tear-off phone numbers. Keep an open mind on what aircraft you are looking for, it may not be the one you had in mind when you started the process. More important than the plane is your compatibility with the co-owners.