FTFBE: A numerical approximation for fuzzy time-fractional Bloch equation
Fractional calculus has a long successful history of 300 years, as it able to model natural phenomena states more accurately than the differential equations of integer order. With this, it plays an important role in variant disciplines. Recently, variant fractional models for the Bloch equations have been proposed, however, effective numerical methods for the fractional Bloch equation (FBE) are still in the infancy stage. In this paper, we extend the time-fractional Bloch equation (TFBE) to fuzzy field under the generalized Caputo differentiability, such that these extensions have natural relationship between crisp. For this purpose, we adopted the fractional Adams-Bashforth-Moulton (FABM) type predictorcorrector method, and introduced a new variant - the fuzzy fractional ADM (FFABM) to find the numerical solution. In this case, a new theorem concerning the error of our proposed FFADM method is also presented. Finally, the capability of the newly developed numerical methods is demonstrated in a fuzzy fractional-order problem, and it achieves satisfactorily in terms of numerical stability.