Solving the fractional order Bloch equation

• DOI: 10.1002/cmr.a.20129
• Publication Date: 2009-01-09T21:47:11Z
• Authors: Richard Magin; Xu Feng; Dumitru Baleanu
• Keywords: Bloch equations; Bloch wave

Abstract Nuclear magnetic resonance (NMR) is a physical phenomenon widely used in chemistry, medicine, and engineering to study complex materials. NMR governed by the Bloch equation, which relates macroscopic model of magnetization applied radiofrequency, gradient static fields. Simple models materials are well described classical first order dynamics precession relaxation inherent vector form equation. Fractional generalization equation presents an opportunity extend its use describe wider range experimental situations involving heterogeneous, porous, or composite Here we terms Caputo fractional derivatives α (0 < 1) for single spin system field at resonance. The results expressed Mittag–Leffler function—a generalized exponential function that converges case when = 1. © 2009 Wiley Periodicals, Inc. Concepts Magn Reson Part A 34A: 16–23, 2009.