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

  • A. S. V. Ravi KanthEmail author
  • Neetu Garg
Conference paper
Part of the Trends in Mathematics book series (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 = (Mx, My, Mz) 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.

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of Technology KurukshetraKurukshetraIndia

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