Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives
The analytical solution of the foam drainage equation with time- and space-fractional derivatives was derived by means of the homotopy analysis method (HAM). The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made; the comparisons show that the...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/237045 |
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| _version_ | 1832545859426844672 |
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| author | Hadi Hosseini Fadravi Hassan Saberi Nik Reza Buzhabadi |
| author_facet | Hadi Hosseini Fadravi Hassan Saberi Nik Reza Buzhabadi |
| author_sort | Hadi Hosseini Fadravi |
| collection | DOAJ |
| description | The analytical solution of the foam drainage equation with time- and space-fractional derivatives was derived by means of the homotopy
analysis method (HAM). The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made; the comparisons
show that the homotopy analysis method is very effective and convenient. By choosing different values of the parameters 𝛼,𝛽 in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. |
| format | Article |
| id | doaj-art-72e83b07fd7c4af9a6f28a7f273e9b6f |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-72e83b07fd7c4af9a6f28a7f273e9b6f2025-02-03T07:24:37ZengWileyInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/237045237045Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional DerivativesHadi Hosseini Fadravi0Hassan Saberi Nik1Reza Buzhabadi2Department of Mathematics, Neyshabour Branch, Islamic Azad University, Neyshabour, IranDepartment of Mathematics, Neyshabour Branch, Islamic Azad University, Neyshabour, IranDepartment of Mathematics, Neyshabour Branch, Islamic Azad University, Neyshabour, IranThe analytical solution of the foam drainage equation with time- and space-fractional derivatives was derived by means of the homotopy analysis method (HAM). The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made; the comparisons show that the homotopy analysis method is very effective and convenient. By choosing different values of the parameters 𝛼,𝛽 in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained.http://dx.doi.org/10.1155/2011/237045 |
| spellingShingle | Hadi Hosseini Fadravi Hassan Saberi Nik Reza Buzhabadi Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives International Journal of Differential Equations |
| title | Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives |
| title_full | Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives |
| title_fullStr | Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives |
| title_full_unstemmed | Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives |
| title_short | Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives |
| title_sort | homotopy analysis method for solving foam drainage equation with space and time fractional derivatives |
| url | http://dx.doi.org/10.1155/2011/237045 |
| work_keys_str_mv | AT hadihosseinifadravi homotopyanalysismethodforsolvingfoamdrainageequationwithspaceandtimefractionalderivatives AT hassansaberinik homotopyanalysismethodforsolvingfoamdrainageequationwithspaceandtimefractionalderivatives AT rezabuzhabadi homotopyanalysismethodforsolvingfoamdrainageequationwithspaceandtimefractionalderivatives |