Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus

The aim of this paper was to first extend the model describing the nonlinear wave movement to the concept of noninteger order derivative. The extended equation was investigated within the scope of an iterative method. The stability and convergence analysis of the iteration method for this extended e...

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Main Authors:	Abdon Atangana, Seyma Tuluce Demiray, Hasan Bulut
Format:	Article
Language:	English
Published:	Hindawi Limited 2014-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2014/481657

id	doaj-63c04e661d404b48aefef6a9096b3550
record_format	Article
spelling	doaj-63c04e661d404b48aefef6a9096b35502020-11-25T01:23:52ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/481657481657Modelling the Nonlinear Wave Motion within the Scope of the Fractional CalculusAbdon Atangana0Seyma Tuluce Demiray1Hasan Bulut2Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South AfricaDepartment of Mathematics, Faculty of Science, Firat University, 23119 Elazig, TurkeyDepartment of Mathematics, Faculty of Science, Firat University, 23119 Elazig, TurkeyThe aim of this paper was to first extend the model describing the nonlinear wave movement to the concept of noninteger order derivative. The extended equation was investigated within the scope of an iterative method. The stability and convergence analysis of the iteration method for this extended equation was presented in detail. The uniqueness of the special solution was also investigated. A resume of the method for solving this equation was provided. The algorithm was used to derive the unique special solution for given initial conditions.http://dx.doi.org/10.1155/2014/481657
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Abdon Atangana Seyma Tuluce Demiray Hasan Bulut
spellingShingle	Abdon Atangana Seyma Tuluce Demiray Hasan Bulut Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus Abstract and Applied Analysis
author_facet	Abdon Atangana Seyma Tuluce Demiray Hasan Bulut
author_sort	Abdon Atangana
title	Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus
title_short	Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus
title_full	Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus
title_fullStr	Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus
title_full_unstemmed	Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus
title_sort	modelling the nonlinear wave motion within the scope of the fractional calculus
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2014-01-01
description	The aim of this paper was to first extend the model describing the nonlinear wave movement to the concept of noninteger order derivative. The extended equation was investigated within the scope of an iterative method. The stability and convergence analysis of the iteration method for this extended equation was presented in detail. The uniqueness of the special solution was also investigated. A resume of the method for solving this equation was provided. The algorithm was used to derive the unique special solution for given initial conditions.
url	http://dx.doi.org/10.1155/2014/481657
work_keys_str_mv	AT abdonatangana modellingthenonlinearwavemotionwithinthescopeofthefractionalcalculus AT seymatulucedemiray modellingthenonlinearwavemotionwithinthescopeofthefractionalcalculus AT hasanbulut modellingthenonlinearwavemotionwithinthescopeofthefractionalcalculus
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Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus

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