Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations

We implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. The fractional derivatives are described in the Caputo sense. These methods are used in a...

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Main Authors: Khaled A. Gepreel, Taher A. Nofal, Fawziah M. Alotaibi
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/482419
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author Khaled A. Gepreel
Taher A. Nofal
Fawziah M. Alotaibi
author_facet Khaled A. Gepreel
Taher A. Nofal
Fawziah M. Alotaibi
author_sort Khaled A. Gepreel
collection DOAJ
description We implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. The fractional derivatives are described in the Caputo sense. These methods are used in applied mathematics to obtain the analytic approximate solutions for the nonlinear Bejamin-Bona Mahoney (BBM) partial fractional differential equation. We compare between the approximate solutions obtained by these methods. Also, we present the figures to compare between the approximate solutions. Also, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved -expansion function method to find exact solutions of nonlinear fractional BBM equation.
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institution Kabale University
issn 1110-757X
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language English
publishDate 2013-01-01
publisher Wiley
record_format Article
series Journal of Applied Mathematics
spelling doaj-art-9730aaccdd3c4a999e15e7482db7593c2025-02-03T01:30:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/482419482419Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential EquationsKhaled A. Gepreel0Taher A. Nofal1Fawziah M. Alotaibi2Mathematics Department, Faculty of Science, Taif University, Taif, Saudi ArabiaMathematics Department, Faculty of Science, Taif University, Taif, Saudi ArabiaMathematics Department, Faculty of Science, Taif University, Taif, Saudi ArabiaWe implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. The fractional derivatives are described in the Caputo sense. These methods are used in applied mathematics to obtain the analytic approximate solutions for the nonlinear Bejamin-Bona Mahoney (BBM) partial fractional differential equation. We compare between the approximate solutions obtained by these methods. Also, we present the figures to compare between the approximate solutions. Also, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved -expansion function method to find exact solutions of nonlinear fractional BBM equation.http://dx.doi.org/10.1155/2013/482419
spellingShingle Khaled A. Gepreel
Taher A. Nofal
Fawziah M. Alotaibi
Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations
Journal of Applied Mathematics
title Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations
title_full Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations
title_fullStr Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations
title_full_unstemmed Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations
title_short Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations
title_sort numerical solutions for the time and space fractional nonlinear partial differential equations
url http://dx.doi.org/10.1155/2013/482419
work_keys_str_mv AT khaledagepreel numericalsolutionsforthetimeandspacefractionalnonlinearpartialdifferentialequations
AT taheranofal numericalsolutionsforthetimeandspacefractionalnonlinearpartialdifferentialequations
AT fawziahmalotaibi numericalsolutionsforthetimeandspacefractionalnonlinearpartialdifferentialequations