A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods
The approximate solutions of the time fractional advection-dispersion equation are presented in this article. The nonlocal nature of solute movement and the nonuniformity of fluid flow velocity in the advection-dispersion process lead to the formation of a heterogeneous system, which can be modeled...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/4856002 |
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| author | Noufe H. Aljahdaly Rasool Shah Muhammed Naeem Mohammad Asif Arefin |
| author_facet | Noufe H. Aljahdaly Rasool Shah Muhammed Naeem Mohammad Asif Arefin |
| author_sort | Noufe H. Aljahdaly |
| collection | DOAJ |
| description | The approximate solutions of the time fractional advection-dispersion equation are presented in this article. The nonlocal nature of solute movement and the nonuniformity of fluid flow velocity in the advection-dispersion process lead to the formation of a heterogeneous system, which can be modeled using a fractional advection-dispersion equation, which generalizes the classical advection-dispersion equation and replaces the time derivative with the fractional Caputo derivative. Researchers use a variety of numerical techniques to study such fractional models, but the nonlocality of the derivative having fractional order leads to high computation complexity and complex calculations, so the task is to find an efficient technique that requires less computation and provides greater accuracy when numerically solving such models. A innovative techniques, homotopy perturbation method and new iteration method, are used in connection with the Elzaki transform to solve the “fractional advection-dispersion equation” which provides the solution in the convergent series form. When the homotopy perturbation method is used with the Elzaki transform, fast convergent series solutions can be obtained with less computation. By solving some cases of time-fractional advection-dispersion equation with varied initial conditions with the help of new iterative transform method and homotopy perturbation transform method demonstrates the usefulness of the proposed methods. |
| format | Article |
| id | doaj-art-c8a0b19a2b7246b4b25801cfea690b00 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-c8a0b19a2b7246b4b25801cfea690b002025-02-03T01:32:26ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/4856002A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical MethodsNoufe H. Aljahdaly0Rasool Shah1Muhammed Naeem2Mohammad Asif Arefin3Mathematics DepartmentDepartment of MathematicsDeanship of Joint First Year Umm Al-Qura University MakkahJashore University of Science and TechnologyThe approximate solutions of the time fractional advection-dispersion equation are presented in this article. The nonlocal nature of solute movement and the nonuniformity of fluid flow velocity in the advection-dispersion process lead to the formation of a heterogeneous system, which can be modeled using a fractional advection-dispersion equation, which generalizes the classical advection-dispersion equation and replaces the time derivative with the fractional Caputo derivative. Researchers use a variety of numerical techniques to study such fractional models, but the nonlocality of the derivative having fractional order leads to high computation complexity and complex calculations, so the task is to find an efficient technique that requires less computation and provides greater accuracy when numerically solving such models. A innovative techniques, homotopy perturbation method and new iteration method, are used in connection with the Elzaki transform to solve the “fractional advection-dispersion equation” which provides the solution in the convergent series form. When the homotopy perturbation method is used with the Elzaki transform, fast convergent series solutions can be obtained with less computation. By solving some cases of time-fractional advection-dispersion equation with varied initial conditions with the help of new iterative transform method and homotopy perturbation transform method demonstrates the usefulness of the proposed methods.http://dx.doi.org/10.1155/2022/4856002 |
| spellingShingle | Noufe H. Aljahdaly Rasool Shah Muhammed Naeem Mohammad Asif Arefin A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods Journal of Function Spaces |
| title | A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods |
| title_full | A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods |
| title_fullStr | A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods |
| title_full_unstemmed | A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods |
| title_short | A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods |
| title_sort | comparative analysis of fractional space time advection dispersion equation via semi analytical methods |
| url | http://dx.doi.org/10.1155/2022/4856002 |
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