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

In this paper, the multi-step differential transform method is employed for the first time to solve a time-fractional 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 from a system of nonlinear ordinary differential equations of fractional order. The fractional derivatives are described in the Caputo sense. The results obtained are in good agreement with the ones in the open literature and it is shown that the technique introduced here is robust, efficient and easy to implement.