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

Mukesh Singh; Mohd Naseem; Amit Kumar; Sunil Kumar

doi:10.1515/nleng-2016-0014

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

Mukesh Singh
, Mohd Naseem
, Amit Kumar
, Sunil Kumar

U.P. Textile Technology Institute
Shri Jagdishprasad Jhabarmal Tibrewala University
National Institute of Technology Jamshedpur

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	161-166
Number of pages	6
Journal	Nonlinear Engineering
Volume	5
Issue number	3
DOIs	https://doi.org/10.1515/nleng-2016-0014
State	Published - 1 Sep 2016
Externally published	Yes

Keywords

Foam drainage model
approximate solution
homotopy analysis transform method
homotopy polynomial

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10.1515/nleng-2016-0014

Cite this

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abstract = "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.",

keywords = "Foam drainage model, approximate solution, homotopy analysis transform method, homotopy polynomial",

author = "Mukesh Singh and Mohd Naseem and Amit Kumar and Sunil Kumar",

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AU - Naseem, Mohd

AU - Kumar, Amit

AU - Kumar, Sunil

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Y1 - 2016/9/1

N2 - 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.

AB - 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.

KW - Foam drainage model

KW - approximate solution

KW - homotopy analysis transform method

KW - homotopy polynomial

UR - https://www.scopus.com/pages/publications/84989204348

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ER -

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

Abstract

Keywords

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