[Here][1] is a thesis containing (in Section 2) an overview of different definitions of fPP. 

My personal favorite is the "Standard Fractional generalization I" defined in 2.2. The reason is that there seems to be (I failed to find any relevant results) an isomorphism between this version and fBm similar to the (usual) Wiener-Poisson isomorphism.


  [1]: http://etd.ohiolink.edu/send-pdf.cgi/Cahoy%2520Dexter%2520Odchigue.pdf?case1180979135%20%22Here%22