An extension of the modified Jiles-Atherton description to include the effect of anisotropy is presented. Anisotropy is related to the value of the angular momentum quantum number J, which affects the form of the Brillouin function used to describe the anhysteretic magnetization. Moreover the shape of magnetization dependent R(m) function is influenced by the choice of the J value.

The fixed-point theorem is widely used in different engineering applications. The present paper focuses on its applications in optimisation. A Matlab toolbox, chich implements the branch-and-bound optimisation method based on the fixed-point theorem, is used for solving different real-life test problems, including estimation of model parameters for the Jiles-Atherton model.