On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation

Recently Caputo and Fabrizio introduced a new derivative with fractional order. In this paper, we presented useful tools about the new derivative and applied it to the nonlinear Fisher’s reaction–diffusion equation. We presented the solution of the modified equation using the notion of iterative met...

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Bibliographic Details
Published in:	Applied mathematics and computation Vol. 273; pp. 948 - 956
Main Author:	Atangana, Abdon
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.01.2016
Subjects:	Caputo–Fabrizio fractional derivative Fixed point theorem New theorems and properties Nonlinear equation Caputo–Fabrizio fractional derivative New theorems and properties Nonlinear equation Fixed point theorem
ISSN:	0096-3003, 1873-5649
Online Access:	Get full text
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Summary:	Recently Caputo and Fabrizio introduced a new derivative with fractional order. In this paper, we presented useful tools about the new derivative and applied it to the nonlinear Fisher’s reaction–diffusion equation. We presented the solution of the modified equation using the notion of iterative method. Using the theory of fixed point, we presented the stability of the used method. Some numerical simulations were presented for different values of fractional order.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2015.10.021