Math. Model. Nat. Phenom.
Volume 16, 2021
Fractional Dynamics in Natural Phenomena
|Number of page(s)||14|
|Published online||03 March 2021|
New aspects of fractional Bloch model associated with composite fractional derivative
Department of Mathematics, JECRC University,
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.
* Corresponding author: firstname.lastname@example.org
Accepted: 4 November 2020
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.
Mathematics Subject Classification: 26A33 / 44A05 / 33E12
Key words: Fractional order Bloch model / nuclear magnetic resonance / magnetization / Hilfer derivative / Sumudu transform / Mittag–Leffler function
© The authors. Published by EDP Sciences, 2021
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