Fatsia Japonica is well able to cope with partial sun, in fact it can be planted in full sun! Have you kept the shrubs well watered and what is the soil like under your oak tree? I think either or both of these are causing the problem not the sun. Unless you dug compost or other organic matter into the ground then the soil is likely to be depleted of nourishment due to the oak tree - what size is the oak tree? Are you aware that Fatsia japonica can grown to 5 yards in height and spread, have you allowed for his much space?

Many parts of the United States where Fatsia grows get hot enough in the afternoon for sunburn to be a real danger. Coastal California, south of Redwood City, is a case in point, and so are the Southeastern States. The only real remedy is to provide artificial shade, or to transplant the bush to a shadier area.
Ricke, can you give us an idea of approximately where in the States you are? It would make suggestions of substitutes much easier.

If you just planted them they might be in a bit of shock from some root damage occurring in that act of planting which is nothing unusual. The days are getting shorter by the minute now, add that to the the angle of the suns rays from the time of initial direct exposure mentioned till the ever quickening sundown decreases the suns effect instead of increasing it. So I don't think that the sun is that much of a factor at all. My advice is stay as you are, be less anxious, and let them take hold to their new surroundings. Give them a year or so and if you don't get what you envisioned move them. You said that you just planted them. Be patient, plants need more time to do what they have to do.