Solutions of the time fractional reaction–diffusion equations with residual power series method

Solutions of the time fractional reaction–diffusion equations with residual power series method

In this article, the residual power series method for solving nonlinear time fractional reaction–diffusion equations is introduced. Residual power series algorithm gets Maclaurin expansion of the solution. The algorithm is tested on Fitzhugh–Nagumo and generalized Fisher equations with nonlinearity...

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Main Authors: Fairouz Tchier, Mustafa Inc, Zeliha S Korpinar, Dumitru Baleanu
Format: Article
Language:English
Published: SAGE Publishing 2016-09-01
Series:Advances in Mechanical Engineering
Online Access:https://doi.org/10.1177/1687814016670867
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spelling doaj-c2691a30c3dc4658b90167fccaa192d92020-11-25T02:55:14ZengSAGE PublishingAdvances in Mechanical Engineering1687-81402016-09-01810.1177/1687814016670867Solutions of the time fractional reaction–diffusion equations with residual power series methodFairouz Tchier0Mustafa Inc1Zeliha S Korpinar2Dumitru Baleanu3Department of Mathematics, King Saud University, Riyadh, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Fırat University, Elazığ, TurkeyDepartment of Administration, Faculty of Economic and Administrative Sciences, Muş Alparslan University, Muş, TurkeyInstitute of Space Sciences, Bucharest, RomaniaIn this article, the residual power series method for solving nonlinear time fractional reaction–diffusion equations is introduced. Residual power series algorithm gets Maclaurin expansion of the solution. The algorithm is tested on Fitzhugh–Nagumo and generalized Fisher equations with nonlinearity ranging. The solutions of our equation are computed in the form of rapidly convergent series with easily calculable components using Mathematica software package. Reliability of the method is given by graphical consequences, and series solutions are used to illustrate the solution. The found consequences show that the method is a powerful and efficient method in determination of solution of the time fractional reaction–diffusion equations.https://doi.org/10.1177/1687814016670867
collection DOAJ
language English
format Article
sources DOAJ
author Fairouz Tchier
Mustafa Inc
Zeliha S Korpinar
Dumitru Baleanu
spellingShingle Fairouz Tchier
Mustafa Inc
Zeliha S Korpinar
Dumitru Baleanu
Solutions of the time fractional reaction–diffusion equations with residual power series method
Advances in Mechanical Engineering
author_facet Fairouz Tchier
Mustafa Inc
Zeliha S Korpinar
Dumitru Baleanu
author_sort Fairouz Tchier
title Solutions of the time fractional reaction–diffusion equations with residual power series method
title_short Solutions of the time fractional reaction–diffusion equations with residual power series method
title_full Solutions of the time fractional reaction–diffusion equations with residual power series method
title_fullStr Solutions of the time fractional reaction–diffusion equations with residual power series method
title_full_unstemmed Solutions of the time fractional reaction–diffusion equations with residual power series method
title_sort solutions of the time fractional reaction–diffusion equations with residual power series method
publisher SAGE Publishing
series Advances in Mechanical Engineering
issn 1687-8140
publishDate 2016-09-01
description In this article, the residual power series method for solving nonlinear time fractional reaction–diffusion equations is introduced. Residual power series algorithm gets Maclaurin expansion of the solution. The algorithm is tested on Fitzhugh–Nagumo and generalized Fisher equations with nonlinearity ranging. The solutions of our equation are computed in the form of rapidly convergent series with easily calculable components using Mathematica software package. Reliability of the method is given by graphical consequences, and series solutions are used to illustrate the solution. The found consequences show that the method is a powerful and efficient method in determination of solution of the time fractional reaction–diffusion equations.
url https://doi.org/10.1177/1687814016670867
work_keys_str_mv AT fairouztchier solutionsofthetimefractionalreactiondiffusionequationswithresidualpowerseriesmethod
AT mustafainc solutionsofthetimefractionalreactiondiffusionequationswithresidualpowerseriesmethod
AT zelihaskorpinar solutionsofthetimefractionalreactiondiffusionequationswithresidualpowerseriesmethod
AT dumitrubaleanu solutionsofthetimefractionalreactiondiffusionequationswithresidualpowerseriesmethod
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