We derive type II supergravity solutions corresponding to space-filling regular and fractional $\mathrm{D}p$ branes on $\left(9\mathrm{}-p\right)$-dimensional conical transverse spaces. Fractional $\mathrm{D}p$-branes are wrapped $\mathrm{D}\mathrm{}(p+2\mathrm{})\mathrm{}$-branes; therefore, our solutions exist only if the base of the cone has a non-vanishing Betti number $b_2.$ We also consider 11-dimensional SUGRA solutions corresponding to regular and fractional M2 branes on 8-dimensional cones whose base has a non-vanishing $b_3.$ (In this case a fractional M2-brane is an M5-brane wrapped over a 3-cycle.) We discuss the gauge theory intepretation of these solutions, as well as of the solutions constructed by Cvetič and co-workers.

• Received 2 February 2001

DOI:https://doi.org/10.1103/PhysRevD.63.126005