New aspects of fractional Bloch model associated with composite fractional derivative

This paper studies a fractional Bloch equation pertaining to Hilfer fractional operator. Bloch equation is broadly applied in physics, chemistry, nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI) and many more. The sumudu transform technique is applied to obtain the analytic solutions for nuclear magnetization M = (M-x, M-y, M-z). The general solution of nuclear magnetization M is shown in the terms of Mittag-Leffler (ML) type function. The influence of order and type of Hilfer fractional operator on nuclear magnetization M is demonstrated in graphical form. The study of Bloch equation with composite fractional derivative reveals the new features of Bloch equation. The discussed fractional Bloch model provides crucial and applicable results to introduce novel information in scientific and technological fields.

Automated summary

This paper investigates a fractional Bloch equation associated with the Hilfer fractional operator, utilizing the Sumudu transform technique to obtain analytical solutions for the nuclear magnetization M. The general solution for M is expressed in terms of Mittag-Leffler (ML) type function, with the influence of order and type of the Hilfer fractional operator on M demonstrated graphically. The study of Bloch equation with composite fractional derivative reveals new features and offers crucial results for introducing novel information in scientific and technological fields.