New aspects of fractional Bloch model associated with composite fractional derivative

Jagdev Singh¹ ; Devendra Kumar² ; Dumitru Baleanu^3, 4

¹ Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India.
² Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India.
³ Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29. Km, Yukarıyurtcu Mahallesi Mimar Sinan Caddesi No: 4 06790, Etimesgut, Turkey.
⁴ Institute of Space Sciences, Magurele-Bucharest, Romania.

Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 10.

Résumé

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 = (Mx, My, Mz). 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.

Détail

DOI : 10.1051/mmnp/2020046

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