Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations

Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations

By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time-fractional Harry Dym equation is presented. Furthermore, num...

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Main Authors: Chao Yue, Guijuan Liu, Kun Li, Hanhui Dong
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2021/6670533
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spelling doaj-a09b23d9e263421889cc332f4561c21f2021-07-02T20:28:55ZengHindawi LimitedAdvances in Mathematical Physics1687-91392021-01-01202110.1155/2021/6670533Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional EquationsChao Yue0Guijuan Liu1Kun Li2Hanhui Dong3College of Medical Information EngineeringCollege of Medical Information EngineeringCollege of Medical Information EngineeringCollege of Medical Information EngineeringBy using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time-fractional Harry Dym equation is presented. Furthermore, numerical solutions of time-fractional diffusion equation are discussed. Again, through another similarity transformation, nonlinear model of space-fractional diffusion/Harry Dym equation is turned into corresponding ordinary differential equations, whose two similarity solutions are also worked out.http://dx.doi.org/10.1155/2021/6670533
collection DOAJ
language English
format Article
sources DOAJ
author Chao Yue
Guijuan Liu
Kun Li
Hanhui Dong
spellingShingle Chao Yue
Guijuan Liu
Kun Li
Hanhui Dong
Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations
Advances in Mathematical Physics
author_facet Chao Yue
Guijuan Liu
Kun Li
Hanhui Dong
author_sort Chao Yue
title Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations
title_short Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations
title_full Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations
title_fullStr Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations
title_full_unstemmed Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations
title_sort similarity solutions to nonlinear diffusion/harry dym fractional equations
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9139
publishDate 2021-01-01
description By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time-fractional Harry Dym equation is presented. Furthermore, numerical solutions of time-fractional diffusion equation are discussed. Again, through another similarity transformation, nonlinear model of space-fractional diffusion/Harry Dym equation is turned into corresponding ordinary differential equations, whose two similarity solutions are also worked out.
url http://dx.doi.org/10.1155/2021/6670533
work_keys_str_mv AT chaoyue similaritysolutionstononlineardiffusionharrydymfractionalequations
AT guijuanliu similaritysolutionstononlineardiffusionharrydymfractionalequations
AT kunli similaritysolutionstononlineardiffusionharrydymfractionalequations
AT hanhuidong similaritysolutionstononlineardiffusionharrydymfractionalequations
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