Approximate‐analytical iterative approach to time‐fractional Bloch equation with Mittag–Leffler type kernel

Abstract

The paper aims to analyze the fractional Bloch equation with Caputo and Atangana–Baleanu–Caputo (ABC) derivative having a nonsingular kernel. The fixed point theorem is used to prove the existence and uniqueness of the proposed equation. Furthermore, the approximate‐analytical solution of the proposed equation is obtained by Aboodh transform iterative method (ATIM) in the form of a convergent series. The technique (ATIM) combines the new iterative method with the Aboodh transform. The convergence analysis of the approximate solution is discussed using the Cauchy convergence theorem. The validity of the ATIM is shown by numerical simulation and graphs. Also, the preference for nonsingular kernel over singular kernel is shown with the help of tables and graphs. For integer order, the obtained solutions from Caputo and ABC derivative are compared with the exact solutions and published work.