A. obesum if one recognizes more than one species. That's because the type specimen of this species is from Aden on the Arabian peninsula. The plants we call A. arabicum are in fact the true A. obesum.
The most helpful identifier of this species is probably the petals that fade from darker on the margins to paler color toward the throat. If nectar guides are present in the throat, they are usually faint. The anther appendages rise to the edge of the throat or a little beyond. This is a potentially evergreen species that can flower at any time of year under tropical conditions. The caudexes range from poorly developed to substantial in different clones, but are never as massive as those of A. arabicum, somalense, or socotranum.
Growing this rare tropical plant in my indoor garden in Chicago has been a big learning experience. When I started hanging around gardening forums and reading about this plant I came across many threads and people that commented on how hard it was to keep this plant alive and healthy. Many people discouraged this plant for beginners to container gardening or for people who don't have don't have a greenhouse or windows that receive full sun.
In the spring and summer I put my plants outdoors and sit them among the other plants in my container garden. Since I'm gardening in a small space and the plants are rather small I place the pots on top of a larger pot. They're heat tolerant plants and like a lot of sun and because of that they get a generous amount of water in the summer whenever I'm watering.
They stay in my outdoor garden among my flowers and other plants but in the fall they start to prepare to be brought into my indoor garden. I don't have plant lights or an indoor plant light set up so they have to make due with sitting in a west facing window. By the time they're brought it they have lost all of their leaves because of the cooler weather and are pretty much dormant. I allow them to go dormant because I don't have grow lights for them and I find it's just easier not to worry about one more plant. During the Adenium Obesum's dormancy I don't water much or any if I can help it because if I did it would spring back to life. The slightest amount of water that I give them after they've been brought in for the winter will start the plant up again. I allow them to get so dry that the caudex ( the trunk) starts to shrink but even then I'll hold back the water.
The plant can be poisonous to people and pets so keep it out of their reach if you want to grow this plant indoors. Last summer my unattended nephew dug out a few chunks from the caudex of one of my Adeniums-lucky nothing happened to either of them. If you want to grow this unusual plant for it's interesting shape it's better to start them from seeds or buy plants that haven't been grafted onto root stock. The fat caudex that everyone likes on this plant can't be achieved with grafting.
Sources: Wikipedia, Wikimedia, Prota4u, Tucsoncactus, Mrbrownthumb