Forecasting the behavior of fractional order Bloch equations appearing in NMR flow via a hybrid computational technique. (November 2022) - Dubey, Ved Prakash; Singh, Jagdev; Alshehri, Ahmed M.; Dubey, Sarvesh; Kumar, Devendra
Abstract: In this paper, we present an efficient computational approach named as Sumudu residual power series method (SRPSM) to solve fractional Bloch equations appearing in an NMR flow. This method is a copulation of the residual power series method (RPSM) and the Sumudu transform to construct approximate solution in shapes of sharp convergent series by adopting the notion of limit with a view of smooth calculations and time saving strategy as compared to the classical RPSM in which computations of fractional derivatives are required. This work also verifies and compares the solution obtained by the proposed technique with the classical RPSM. To assure the applicability, performance, and reliability of the introduced method, a system of fractional Bloch equations are examined along with numerical simulations. The aspect of application supported with computer simulations demonstrates that the suggested approach is precise, and appropriate to explore the solutions of linear & nonlinear initial value problems with fractional-order derivatives. Highlights: Fractional Bloch equations appearing in an NMR flow are studied. A hybrid computational technique is used to slove the fractional order problem. The method is a combination of residual power series method and the sumudu transform. The results for fractional Bloch equations are presented graphically.