SPICE simulation of fractional order element without using Ladder circuit

Recent trend of research area got priority to use fractional order elements in different areas of science and engineering. So far multi-component fractional order elements (ladder fractor) are implemented using SPICE simulation as there is no tool box in SPICE for fractional elements implementation. If the ladder fractor is used, the circuit becomes complicated that may stop the circuit simulation. In this context, single component fractional order elements have been simulated for the first time using control voltage source (E) in SPICE for different practical circuits. Characteristics of the circuit using fractional inductor can be easily analysed as single component fractional inductor which has not yet fabricated. It has been shown that using this simulation method, fractional order circuits can be realized easily for the entire frequency range for different $\alpha$ values. For comparative studies single component fractional capacitors fabricated in IIT Kharagpur, have been used for circuit realization.