Modeling and numerical analysis of fractional-order Bloch equations

This paper deals with the Bloch equations which are a set of macroscopic equations that are used for modeling of nuclear magnetization as a function of time. These equations were introduced by Felix Bloch in 1946 and they are used for a description of the Nuclear Magnetic Resonance (NMR). This physical phenomenon is used in medicine, chemistry, physics, and engineering to study complex material. Fractional-order generalization of the Bloch equations was presented by Richard Magin et al. in 2008 as an opportunity to extend their use to describe a wider range of experimental situations involving heterogeneous, porous, or composite materials. In this paper we describe numerical and simulation models (created for Matlab/ Simulink) of the classical and the fractional-order Bloch equations. The behaviour and stability analysis of the Bloch equations are presented as well.