Fixed-point theorem for Caputo--Fabrizio fractional Nagumo equation with nonlinear diffusion and convection
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Authors
Rubayyi T. Alqahtani
- Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), P. O. Box 65892, Riyadh 11566, Saudi Arabia.
Abstract
We make use of fractional derivative, recently proposed by Caputo and Fabrizio, to modify the nonlinear Nagumo diffusion and convection equation. The proposed fractional derivative has no singular kernel
considered as a filter. We examine the existence of the exact solution of the modified equation using the
method of fixed-point theorem. We prove the uniqueness of the exact solution and present some numerical
simulations.
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ISRP Style
Rubayyi T. Alqahtani, Fixed-point theorem for Caputo--Fabrizio fractional Nagumo equation with nonlinear diffusion and convection, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 1991--1999
AMA Style
Alqahtani Rubayyi T., Fixed-point theorem for Caputo--Fabrizio fractional Nagumo equation with nonlinear diffusion and convection. J. Nonlinear Sci. Appl. (2016); 9(5):1991--1999
Chicago/Turabian Style
Alqahtani, Rubayyi T.. "Fixed-point theorem for Caputo--Fabrizio fractional Nagumo equation with nonlinear diffusion and convection." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 1991--1999
Keywords
- Nonlinear Nagumo equation
- Caputo-Fabrizio derivative
- fixed-point theorem
- uniqueness.
MSC
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