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Analytical solutions of the Keller-Segel chemotaxis model involving fractional operators without singular kernel

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Abstract.

This paper discusses the application of analytical techniques, namely the Laplace homotopy perturbation method and the modified homotopy analysis transform method, for solving a coupled one-dimensional time-fractional Keller-Segel chemotaxis model. The first method is based on a combination of the Laplace transform and homotopy methods, while the second method is an analytical technique based on the homotopy polynomial. Fractional derivatives with exponential and Mittag-Leffler laws in Liouville-Caputo sense are considered. The effectiveness of both methods is demonstrated by finding the exact solutions of the Keller-Segel chemotaxis model. Some examples have been presented in order to compare the results obtained with both fractional-order derivatives.

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Authors and Affiliations

  1. Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria, Chilpancingo, Guerrero, Mexico

    V. F. Morales-Delgado & M. A. Taneco-Hernández

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

    J. F. Gómez-Aguilar

  3. Department of Mathematics, National Institute of Technology, Jamshedpur, 831014, Jharkhand, India

    Sunil Kumar

Authors
  1. V. F. Morales-Delgado
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  2. J. F. Gómez-Aguilar
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  3. Sunil Kumar
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  4. M. A. Taneco-Hernández
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Correspondence to J. F. Gómez-Aguilar.

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Morales-Delgado, V.F., Gómez-Aguilar, J.F., Kumar, S. et al. Analytical solutions of the Keller-Segel chemotaxis model involving fractional operators without singular kernel. Eur. Phys. J. Plus 133, 200 (2018). https://doi.org/10.1140/epjp/i2018-12038-6

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