# Fixed-point theorem for Caputo--Fabrizio fractional Nagumo equation with nonlinear diffusion and convection

Volume 9, Issue 5, pp 1991--1999 Publication Date: May 20, 2016
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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.

### Keywords

• Nonlinear Nagumo equation
• Caputo-Fabrizio derivative
• fixed-point theorem
• uniqueness.

•  47H10
•  34A08

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