Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equat...

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Main Authors: A. Elsaid, M. S. Abdel Latif, M. Maneea
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2016/7304659
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spelling doaj-cc21800b364a42d9b5c679368b6d04512021-07-02T06:41:17ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/73046597304659Similarity Solutions for Multiterm Time-Fractional Diffusion EquationA. Elsaid0M. S. Abdel Latif1M. Maneea2Mathematics & Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura 35516, EgyptMathematics & Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura 35516, EgyptMathematics & Engineering Physics Department, Faculty of Engineering, Modern University for Technology and Information, Cairo 11585, EgyptSimilarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on the obtained results, we propose a definition for a multiterm error function with generalized coefficients.http://dx.doi.org/10.1155/2016/7304659
collection DOAJ
language English
format Article
sources DOAJ
author A. Elsaid
M. S. Abdel Latif
M. Maneea
spellingShingle A. Elsaid
M. S. Abdel Latif
M. Maneea
Similarity Solutions for Multiterm Time-Fractional Diffusion Equation
Advances in Mathematical Physics
author_facet A. Elsaid
M. S. Abdel Latif
M. Maneea
author_sort A. Elsaid
title Similarity Solutions for Multiterm Time-Fractional Diffusion Equation
title_short Similarity Solutions for Multiterm Time-Fractional Diffusion Equation
title_full Similarity Solutions for Multiterm Time-Fractional Diffusion Equation
title_fullStr Similarity Solutions for Multiterm Time-Fractional Diffusion Equation
title_full_unstemmed Similarity Solutions for Multiterm Time-Fractional Diffusion Equation
title_sort similarity solutions for multiterm time-fractional diffusion equation
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2016-01-01
description Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on the obtained results, we propose a definition for a multiterm error function with generalized coefficients.
url http://dx.doi.org/10.1155/2016/7304659
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AT msabdellatif similaritysolutionsformultitermtimefractionaldiffusionequation
AT mmaneea similaritysolutionsformultitermtimefractionaldiffusionequation
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