Next Article in Journal
Modeling Soil Moisture Profiles in Irrigated Fields by the Principle of Maximum Entropy
Next Article in Special Issue
Power-Type Functions of Prediction Error of Sea Level Time Series
Previous Article in Journal
Detecting Chronotaxic Systems from Single-Variable Time Series with Separable Amplitude and Phase
Open AccessArticle

Analysis of the Keller–Segel Model with a Fractional Derivative without Singular Kernel

1
Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300 Bloemfontein, South Africa
2
Department of Mathematics, Colleges of Sciences, King Saud University, P.O. Box 1142, Riyadh, 11989, Saudi Arabia
*
Author to whom correspondence should be addressed.
Academic Editor: Carlo Cattani
Entropy 2015, 17(6), 4439-4453; https://doi.org/10.3390/e17064439
Received: 15 May 2015 / Revised: 5 June 2015 / Accepted: 9 June 2015 / Published: 23 June 2015
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory I)
Using some investigations based on information theory, the model proposed by Keller and Segel was extended to the concept of fractional derivative using the derivative with fractional order without singular kernel recently proposed by Caputo and Fabrizio. We present in detail the existence of the coupled-solutions using the fixed-point theorem. A detailed analysis of the uniqueness of the coupled-solutions is also presented. Using an iterative approach, we derive special coupled-solutions of the modified system and we present some numerical simulations to see the effect of the fractional order. View Full-Text
Keywords: Keller–Segel model; Caputo–Fabrizio fractional derivative; fixed-point theorem; special solution Keller–Segel model; Caputo–Fabrizio fractional derivative; fixed-point theorem; special solution
MDPI and ACS Style

Atangana, A.; Alkahtani, B.S.T. Analysis of the Keller–Segel Model with a Fractional Derivative without Singular Kernel. Entropy 2015, 17, 4439-4453.

Show more citation formats Show less citations formats

Article Access Map by Country/Region

1
Only visits after 24 November 2015 are recorded.
Back to TopTop