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 inApplied mathematics and computation Vol. 273; pp. 948 - 956
Main Author Atangana, Abdon
Format Journal Article
LanguageEnglish
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
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ISSN0096-3003
1873-5649
DOI10.1016/j.amc.2015.10.021

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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