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Model of Coupled System of Fractional Reaction-Diffusion Within a New Fractional Derivative Without Singular Kernel

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Fractional Derivatives with Mittag-Leffler Kernel

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 194))

Abstract

In this chapter, the approximate analytical solutions of a new reaction-diffusion fractional time model are studied. For this analysis is used the p-homotopy transform method based on different kernels (power, exponential and Mittag-Leffler). The system nonlinearities are addressed by the Adomian polynomials. The system convergence is studied by determining the interval of the convergence by \(\hbar \)-curves, as well as, searching for the optimal value of \(\hbar \) which minimize the residual error. Therefore, the optimal \(\hbar \) value is calculated to estimate the order \(\beta \) error. At the end of the chapter, we explained the obtained behavior by plotting the solutions in 3D. The results are accurate.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of South Africa, Florida, 0003, South Africa

    K. M. Saad

  2. CONACYT-Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Interna del Internado, Palmira, 62490, Cuernavaca, Morelos, México

    J. F. Gómez-Aguilar

  3. Faculty of Natural and Agricultural Sciences, Institute of Groundwater Studies, University of Free State, Bloemfontein, 9301, South Africa

    A. Atangana

  4. Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Interna del Internado, Palmira, 62490, Cuernavaca, Morelos, México

    R. F. Escobar-Jiménez

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  1. K. M. Saad
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  2. J. F. Gómez-Aguilar
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  3. A. Atangana
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  4. R. F. Escobar-Jiménez
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Correspondence to J. F. Gómez-Aguilar .

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Editors and Affiliations

  1. CONACYT-Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Morelos, Mexico

    José Francisco Gómez

  2. CONACYT-Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Lizeth Torres

  3. Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Morelos, Mexico

    Ricardo Fabricio Escobar

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Saad, K.M., Gómez-Aguilar, J.F., Atangana, A., Escobar-Jiménez, R.F. (2019). Model of Coupled System of Fractional Reaction-Diffusion Within a New Fractional Derivative Without Singular Kernel. In: Gómez, J., Torres, L., Escobar, R. (eds) Fractional Derivatives with Mittag-Leffler Kernel. Studies in Systems, Decision and Control, vol 194. Springer, Cham. https://doi.org/10.1007/978-3-030-11662-0_17

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  • DOI: https://doi.org/10.1007/978-3-030-11662-0_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11661-3

  • Online ISBN: 978-3-030-11662-0

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