New aspects of fractional Bloch model associated with composite fractional derivative

Singh Jagdev; Kumar Devendra; Baleanu Dumitru

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New aspects of fractional Bloch model associated with composite fractional derivative

机译：与复合分数衍生物相关的分数布洛赫模型的新方面

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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.

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来源
《Mathematical modelling of natural phenomena》 |2021年第1期|共14页
作者
Singh Jagdev; Kumar Devendra; Baleanu Dumitru;
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作者单位

JECRC Univ Dept Math Jaipur 303905 Rajasthan India;

Univ Rajasthan Dept Math Jaipur 302004 Rajasthan India;

Cankaya Univ Fac Arts &

Sci Dept Math Eskisehir Yolu 29 Km Yukariyurtcu Mahallesi Mimar TR-06790 Etimesgut Turkey;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Fractional order Bloch model; nuclear magnetic resonance; magnetization; Hilfer derivative; Sumudu transform; Mittag-Leffler function;

机译：小数秩序Bloch模型;核磁共振;磁化;海事衍生物;Sumudu变换;Mittag-Leffler函数;

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11. Analysis of Acoustic Loss Models with Fractional Time Derivatives using the Similarity Transformation Approach. [R] . Verweij, M. D. 2000

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New aspects of fractional Bloch model associated with composite fractional derivative

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