Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method

The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, lineari...

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Main Authors:	Zhoujin Cui, Zisen Mao, Sujuan Yang, Pinneng Yu
Format:	Article
Language:	English
Published:	Hindawi Limited 2013-01-01
Series:	Mathematical Problems in Engineering
Online Access:	http://dx.doi.org/10.1155/2013/186934

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spelling	doaj-b2a7e4ec2b0043cda2aef0ef122697302020-11-24T22:47:15ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472013-01-01201310.1155/2013/186934186934Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation MethodZhoujin Cui0Zisen Mao1Sujuan Yang2Pinneng Yu3Jiangsu Maritime Institute, Nanjing 211100, ChinaInstitute of Science, PLA University of Science and Technology, Nanjing 211101, ChinaInstitute of Science, PLA University of Science and Technology, Nanjing 211101, ChinaInstitute of Science, PLA University of Science and Technology, Nanjing 211101, ChinaThe approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The two different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance.http://dx.doi.org/10.1155/2013/186934
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Zhoujin Cui Zisen Mao Sujuan Yang Pinneng Yu
spellingShingle	Zhoujin Cui Zisen Mao Sujuan Yang Pinneng Yu Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method Mathematical Problems in Engineering
author_facet	Zhoujin Cui Zisen Mao Sujuan Yang Pinneng Yu
author_sort	Zhoujin Cui
title	Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method
title_short	Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method
title_full	Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method
title_fullStr	Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method
title_full_unstemmed	Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method
title_sort	approximate analytical solutions of fractional perturbed diffusion equation by reduced differential transform method and the homotopy perturbation method
publisher	Hindawi Limited
series	Mathematical Problems in Engineering
issn	1024-123X 1563-5147
publishDate	2013-01-01
description	The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The two different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance.
url	http://dx.doi.org/10.1155/2013/186934
work_keys_str_mv	AT zhoujincui approximateanalyticalsolutionsoffractionalperturbeddiffusionequationbyreduceddifferentialtransformmethodandthehomotopyperturbationmethod AT zisenmao approximateanalyticalsolutionsoffractionalperturbeddiffusionequationbyreduceddifferentialtransformmethodandthehomotopyperturbationmethod AT sujuanyang approximateanalyticalsolutionsoffractionalperturbeddiffusionequationbyreduceddifferentialtransformmethodandthehomotopyperturbationmethod AT pinnengyu approximateanalyticalsolutionsoffractionalperturbeddiffusionequationbyreduceddifferentialtransformmethodandthehomotopyperturbationmethod
_version_	1725682419207503872

Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method

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