Numerical simulation for fractional Bloch equation arising in nuclear magnetic resonance

Abstract

This paper deals with fractional model of Bloch equation in Nuclear Magnetic Resonance (NMR). The applications of NMR are magnetic resonance imaging (MRI) for medical diagnosis, magnetic resonance microscopy (MRM) in research settings, chemists can determine the structure of many compounds and for analysing expansive biological samples like nucleic acids, RNA, DNA and proteins. Here, we present a numerical algorithm using Chebyshev polynomial of third kind for the numerical solution of integer and fractional order Bloch equation. Entire trajectory of magnetization is shown in 3D for integer and fractional order Bloch equation. The dynamic of magnetization is also shown for integer and fractional order relaxation. Obtained numerical results are simulated with known solutions. We also compared results with known solutions.  Errors tables are used to show the accuracy of the method.