Homotopy analysis transform algorithm to solve time-fractional foam drainage equation

Homotopy analysis transform algorithm to solve time-fractional foam drainage equation

This paper emphasizes on finding the solution for a foam drainageequation using the technique of modified homotopy analysis transform method (MHATM). MHATM is a new amalgamation of the homotopy analysis method and Laplace transform method with homotopy polynomial. Comparisons are made between the re...

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Main Authors: Singh Mukesh, Naseem Mohd, Kumar Amit, Kumar Sunil
Format: Article
Language:English
Published: De Gruyter 2016-09-01
Series:Nonlinear Engineering
Subjects:
foam drainage model
homotopy analysis transform method
homotopy polynomial
approximate solution
Online Access:https://doi.org/10.1515/nleng-2016-0014
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spelling doaj-7bbf10d885064d81bf46ebb500c698602021-09-06T19:21:06ZengDe GruyterNonlinear Engineering2192-80102192-80292016-09-015316116610.1515/nleng-2016-0014Homotopy analysis transform algorithm to solve time-fractional foam drainage equationSingh Mukesh0Naseem Mohd1Kumar Amit2Kumar Sunil3Shri Jagdishprasad Jhabarmal Tibrewala University, Jhunjhunu-333001, Rajasthan, IndiaDepartment of Basic Science, UP Textile Technology Institute, Kanpur-208001, Uttar Pradesh, IndiaDepartment of Mathematics, National Institute of Technology, Jamshedpur-831014, Jharkhand, IndiaDepartment of Mathematics, National Institute of Technology, Jamshedpur-831014, Jharkhand, IndiaThis paper emphasizes on finding the solution for a foam drainageequation using the technique of modified homotopy analysis transform method (MHATM). MHATM is a new amalgamation of the homotopy analysis method and Laplace transform method with homotopy polynomial. Comparisons are made between the results of the proposed method for different values of fractional derivative α and exact solutions. Then, we analyze the results by numerical simulations, which demonstrate the simplicity and effectiveness of the present method.https://doi.org/10.1515/nleng-2016-0014foam drainage modelhomotopy analysis transform methodhomotopy polynomialapproximate solution
collection DOAJ
language English
format Article
sources DOAJ
author Singh Mukesh
Naseem Mohd
Kumar Amit
Kumar Sunil
spellingShingle Singh Mukesh
Naseem Mohd
Kumar Amit
Kumar Sunil
Homotopy analysis transform algorithm to solve time-fractional foam drainage equation
Nonlinear Engineering
foam drainage model
homotopy analysis transform method
homotopy polynomial
approximate solution
author_facet Singh Mukesh
Naseem Mohd
Kumar Amit
Kumar Sunil
author_sort Singh Mukesh
title Homotopy analysis transform algorithm to solve time-fractional foam drainage equation
title_short Homotopy analysis transform algorithm to solve time-fractional foam drainage equation
title_full Homotopy analysis transform algorithm to solve time-fractional foam drainage equation
title_fullStr Homotopy analysis transform algorithm to solve time-fractional foam drainage equation
title_full_unstemmed Homotopy analysis transform algorithm to solve time-fractional foam drainage equation
title_sort homotopy analysis transform algorithm to solve time-fractional foam drainage equation
publisher De Gruyter
series Nonlinear Engineering
issn 2192-8010
2192-8029
publishDate 2016-09-01
description This paper emphasizes on finding the solution for a foam drainageequation using the technique of modified homotopy analysis transform method (MHATM). MHATM is a new amalgamation of the homotopy analysis method and Laplace transform method with homotopy polynomial. Comparisons are made between the results of the proposed method for different values of fractional derivative α and exact solutions. Then, we analyze the results by numerical simulations, which demonstrate the simplicity and effectiveness of the present method.
topic foam drainage model
homotopy analysis transform method
homotopy polynomial
approximate solution
url https://doi.org/10.1515/nleng-2016-0014
work_keys_str_mv AT singhmukesh homotopyanalysistransformalgorithmtosolvetimefractionalfoamdrainageequation
AT naseemmohd homotopyanalysistransformalgorithmtosolvetimefractionalfoamdrainageequation
AT kumaramit homotopyanalysistransformalgorithmtosolvetimefractionalfoamdrainageequation
AT kumarsunil homotopyanalysistransformalgorithmtosolvetimefractionalfoamdrainageequation
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