This paper proposes the design of fractional order(FO) Butter worth filter in complex wplane (w=s^q; q being any real number) considering the presence of under-damped, hyper- damped, ultra-damped poles. This is the first attempt to design such fractional Butter- worth filters in complex w-plane instead of complex s-plane, as conventionally done for integer order filters. First, the concept of fractional derivatives and w-plane stability of linear fractional order systems are discussed. Detailed mathematical formulation for the design of fractional Butter worth-like filter (FBWF) in w-plane is then presented. Simulation examples are given along with a practical example to design the FO Butterworth filter with given specifications in frequency domain to show the practicability of the proposed formulation.