SummaryBy using the fractional‐order medium constitutive relations and Maxwell equations, the modeling and theoretical analysis of the fractional‐order inductor (FOI) is investigated in this study. The general formulations of the magnetic property model of FOI core material are derived. This paper proposes a generalized approach to design and implement a single‐component FOI and constructs the independent fractional‐order circuit element in Matlab/Simulink based on the fractional calculus Grünwald–Letnikov (GL) definition. The electrical and magnetic performance of the FOI are characterized in both frequency and time domain by simulation and experimentation. All results show that it is effective to use the proposed method and design guidance to construct the FOI. Furthermore, the results from the application of FOI in the fractional‐orderRLλCseries‐resonance circuit show that the order has an effect on the characteristics and frequency properties of it.