If it is already proven that autonomous fractional-order systems cannot have exact periodic solutions, then is it still okay to talk about almost periodic or repeating-like patterns that we see in numerical simulations?
Yes, repeating patterns in simulations can be discussed even if strict periodicity is impossible in autonomous fractional systems, since quasi-periodic or recurrent dynamics can still provide insights into stability, attractor behavior, and long-term system trends without requiring exact periodic repetition.