MODELING AND APPLICATIONS OF FRACTIONAL-ORDER MUTUAL INDUCTANCE BASED ON ATANGANA–BALEANU AND CAPUTO–FABRIZIO FRACTIONAL DERIVATIVES

Abstract

Many electrical systems can be characterized more authentically by fractional-order dynamic systems. The Atangana–Baleanu and the Caputo–Fabrizio fractional derivatives have solved the singularity problem in Caputo derivative. This work uses Atangana–Baleanu and Caputo–Fabrizio fractional derivatives to model the fractional-order mutual inductance in the frequency domain. To use the fractional mutual inductance in circuit design, the T-model equivalent circuits are presented with different fractional derivatives. The fractional impedance matching networks based on proposed fractional mutual coupling circuits are simulated as an application. The impedance characteristics of networks with different fractional orders are analyzed. The results indicate that the proposed fractional mutual coupling circuits based on Atangana–Baleanu and Caputo–Fabrizio fractional derivatives can be applied to the complex electrical systems to increase the design degree of freedom, which provides more choices for describing the nonlinear characteristics of the system.