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

• Published in: European physical journal plus Vol. 133; no. 5; p. 200
• Main Authors: Morales-Delgado, V. F., Gómez-Aguilar, J. F., Kumar, Sunil, Taneco-Hernández, M. A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-05-2018; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Calculus; Complex Systems; Condensed Matter Physics; Exact solutions; Fractional calculus; Homotopy theory; Laplace transforms; Mathematical and Computational Physics; Methods; Molecular; Operators (mathematics); Optical and Plasma Physics; Perturbation methods; Physics; Physics and Astronomy; Polynomials; Regular Article; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/i2018-12038-6

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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.