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On the New Fractional Operator and Application to Nonlinear Bloch System

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Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 272))

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Abstract

In this chapter, we analyze the nonlinear Bloch system with a new fractional operator without singular kernel proposed by Michele Caputo and Mauro Fabrizio. The commensurate and non-commensurate order nonlinear Bloch system is considered. Special solutions using a numerical scheme based in Lagrange interpolations were obtained. We studied the uniqueness and existence of the solutions employing the fixed point theorem. Novel chaotic attractors with total order less than 3 are obtained.

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Acknowledgements

José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.

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Authors and Affiliations

  1. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico

    J. F. Gómez-Aguilar

  2. Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran

    Behzad Ghanbari

  3. Department of Mathematics Education, University of Education Winneba (Kumasi Campus), Winneba, Ghana

    Ebenezer Bonyah

Authors
  1. J. F. Gómez-Aguilar
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  2. Behzad Ghanbari
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  3. Ebenezer Bonyah
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Contributions

All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

Corresponding author

Correspondence to J. F. Gómez-Aguilar .

Editor information

Editors and Affiliations

  1. Department of Mathematics, JECRC University, Jaipur, Rajasthan, India

    Jagdev Singh

  2. Department of Mathematics, University of Rajasthan, Jaipur, Rajasthan, India

    Devendra Kumar

  3. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  4. Department of Mathematics, Cankaya University, Balgat, Ankara, Turkey

    Dumitru Baleanu

  5. Department of Mathematics, Rajasthan Technical University, Kota, Rajasthan, India

    Sunil Dutt Purohit

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Gómez-Aguilar, J.F., Ghanbari, B., Bonyah, E. (2019). On the New Fractional Operator and Application to Nonlinear Bloch System. In: Singh, J., Kumar, D., Dutta, H., Baleanu, D., Purohit, S. (eds) Mathematical Modelling, Applied Analysis and Computation. ICMMAAC 2018. Springer Proceedings in Mathematics & Statistics, vol 272. Springer, Singapore. https://doi.org/10.1007/978-981-13-9608-3_9

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