Quantitative MR relaxation using MR fingerprinting with fractional-order signal evolution.The fractional-order Bloch equations have been shown to describe a wider range of experimental situations involving heterogeneous, porous, or composite materials.  This paper introduces a novel dictionary of quantitative MR fingerprinting generated by signal evolution model with fractional-order Bloch equations to describe magnetic resonance (MR) relaxation.  So the proposed method can provide well extensions of current MR fingerprinting and has shown potential to apply into the phantom experiments and the in vivo applications to approach the standard methods for quantitative imaging.
MR fingerprinting
Here, the fractional-order relaxation models are implemented into Bloch equations through phase transitions using EPG simulation. 
EPG simulation