Not sure about about Simulink (as I've never used it), but in Matlab you should be able to simulate Randle's circuit by coding Warbug element (ZW = AW/(jω)^0.5) manually into your equivalent circuit code.
I was about to suggest not to use the transfer function but I see that you indicated that is not possible. Have you tried attempting s^(-1/2) instead? (I do not have MATLAB in handy so cannot check myself for now).