Analytical Solutions of the Bloch Equation via Fractional Operators with Non-singular Kernels

摘要

This article deals with the fractional Bloch equation by using Caputo-Fabrizio fractional derivative and Atangana-Baleanu fractional derivative with non-singular kernels. Bloch equation is extensively used in chemistry, physics, magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR). The nuclear magnetization M = (M_x, M_y, M_z) is derived analytically, and its behaviour is discussed via plots for different fractional orders. A comparative study of the analytical solutions with Caputo-Fabrizio, Atangana-Baleanu and Caputo fractional derivatives is presented. Equilibrium stage is achieved faster via Atangana-Baleanu fractional derivative than other fractional derivatives.