Issue |
Math. Model. Nat. Phenom.
Volume 16, 2021
Fractional Dynamics in Natural Phenomena
|
|
---|---|---|
Article Number | 10 | |
Number of page(s) | 14 | |
DOI | https://doi.org/10.1051/mmnp/2020046 | |
Published online | 03 March 2021 |
New aspects of fractional Bloch model associated with composite fractional derivative
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.
* Corresponding author: devendra.maths@gmail.com
Received:
28
August
2020
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.