The introduction of autonomous vehicles (AVs) to consumer markets will expedite the trend of car sharing and enable co-owning or co-leasing a car. In this paper, we consider a combinatorial auction market for fractional ownership of AVs, which is unique in two aspects. First, items are neither predefined nor discrete; rather, items are continuous time slots defined by bidders. Second, the spatial information of bidders should be incorporated within the winner determination problem (WDP) so that sharing a vehicle is indeed a viable plan. The consideration of spatial information increases the computational complexity significantly. We formulate the WDP, which plays a critical role in various auction designs and pricing schemes, for both discrete- and continuous-time settings. In terms of social welfare maximization, we show that the continuous-time model is superior to the discrete-time model. We provide a conflict-based reformulation of the continuous-time model, for which we develop an effective solution approach based on a heuristic and maximal clique based reformulations. Using samples of the 2010-2012 California Household Travel Survey, we verify that the proposed solution methods provide effective computational tools for the combinatorial auction with bidder-defined items.