Solving the fractional nonlinear Bloch system using multi-step generalizeddifferential transform method

摘要

In this paper, the multi-step differential transform method is first employed to solve a timefractional nonlinear Bloch system. The nonlinear Bloch equation is known to govern the dynamics of an ensemble of spins, controlling the basic process of nuclear magnetic resonance (NMR). This nonlinear Bloch equation is formed by a system of nonlinear ordinary differential equations of fractional order. The fractional derivatives are described in the Caputo sense. The obtained results are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, efficient and easy to implement.