- My understanding about fractional order system is that it can have poles on the right hand side of imaginary axis in s-plane and yet being stable. (statement 1)
There are other theorems about stability that cannot be true at the same time with statement 1.
The second understanding is that Region Of Convergence (ROC) of Laplace transform is including vertical lines regardless of being fractional order or integer order (statement 2).
Third understanding is that the ROC of an LTI causal system is at the right hand side of all of its poles regardless of being integer of fractional order. (statement 3)
And 4rth understanding is that for all causal stable LTI system, the ROC includes $j\omega$ axis regardless of system being fractional order or integer order. (statement 4)
These statements cannot be correct all at the same time because if the ROC is at the right hand side of poles in a vertical way and poles can be at right hand side of imaginary axis, then the ROC of a fractional order stable causal system may not include the imaginary axis anymore.
How can these statements be correct at the same time? or which of them have a mistake?
Unfortunately, I do not have any software that plots fractional order ROC for me.
How is it possible?