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Analytical Solutions of the Bloch Equation via Fractional Operators with Non-singular Kernels

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Applied Mathematics and Scientific Computing

Part of the book series: Trends in Mathematics ((TM))

Abstract

This article deals with the fractional Bloch equation by using Caputo-Fabrizio fractional derivative and Atangana-Baleanu fractional derivative with non-singular kernels. Bloch equation is extensively used in chemistry, physics, magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR). The nuclear magnetization M = (M x, M y, M z) is derived analytically, and its behaviour is discussed via plots for different fractional orders. A comparative study of the analytical solutions with Caputo-Fabrizio, Atangana-Baleanu and Caputo fractional derivatives is presented. Equilibrium stage is achieved faster via Atangana-Baleanu fractional derivative than other fractional derivatives.

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Acknowledgements

The second author acknowledges the University Grants Commission of India for providing financial support for the above research (Sr.No. 2061440951, reference no.22/06/14(i)EU-V). The authors would like to thank the anonymous reviewers for their valuable suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Kurukshetra, Kurukshetra, Haryana, India

    A. S. V. Ravi Kanth & Neetu Garg

Authors
  1. A. S. V. Ravi Kanth
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  2. Neetu Garg
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Corresponding author

Correspondence to A. S. V. Ravi Kanth .

Editor information

Editors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    B. Rushi Kumar

  2. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    R. Sivaraj

  3. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    B. S. R. V. Prasad

  4. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    M. Nalliah

  5. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    A. Subramanyam Reddy

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Ravi Kanth, A.S.V., Garg, N. (2019). Analytical Solutions of the Bloch Equation via Fractional Operators with Non-singular Kernels. In: Rushi Kumar, B., Sivaraj, R., Prasad, B., Nalliah, M., Reddy, A. (eds) Applied Mathematics and Scientific Computing. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01123-9_5

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