Fractional operators for the magnetic dynamic behavior of ferromagnetic specimens: An overview

This paper reviews the use of the fractional derivative operators for the dynamic magnetization of ferromagnetic specimens. Magnetic behaviors in ferromagnetic specimens are strongly nonlinear and frequency dependent. Magnetism has an atomic origin but the magnetic behavior as observed at the human scale is highly affected by phenomena occurring at larger scales. Under the influence of an external magnetic field, the homogeneity of a ferromagnetic sample magnetization is linked to the excitation dynamics. Models and simulations in this domain are strongly needed, as they provide theoretical explanations and allow us to anticipate complex phenomena, difficult to observe in a practical way. On the one hand, such multi-scale dynamical behaviors can hardly be taken into account with the usual mathematical operators. On the other hand, correct simulation results on large frequency bandwidths can be obtained using fractional derivative operators. The use of fractional derivatives can be envisaged through different approaches: Lump models based on time fractional differential equations is one option, and fractional anomalous diffusion equations is another. In this manuscript, these two methods are detailed and compared. Theoretical results are compared to experimental ones, and conclusions and perspectives are drawn such as possible improvements.