A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation
In this manuscript, a semianalytical solution of the time-fractional Navier-Stokes equation under Caputo fractional derivatives using Optimal Homotopy Asymptotic Method (OHAM) is proposed. The above-mentioned technique produces an accurate approximation of the desired solutions and hence is known as...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/5547804 |
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| author | Zeeshan Ali Shayan Naseri Nia Faranak Rabiei Kamal Shah Ming Kwang Tan |
| author_facet | Zeeshan Ali Shayan Naseri Nia Faranak Rabiei Kamal Shah Ming Kwang Tan |
| author_sort | Zeeshan Ali |
| collection | DOAJ |
| description | In this manuscript, a semianalytical solution of the time-fractional Navier-Stokes equation under Caputo fractional derivatives using Optimal Homotopy Asymptotic Method (OHAM) is proposed. The above-mentioned technique produces an accurate approximation of the desired solutions and hence is known as the semianalytical approach. The main advantage of OHAM is that it does not require any small perturbations, linearization, or discretization and many reductions of the computations. Here, the proposed approach’s reliability and efficiency are demonstrated by two applications of one-dimensional motion of a viscous fluid in a tube governed by the flow field by converting them to time-fractional Navier-Stokes equations in cylindrical coordinates using fractional derivatives in the sense of Caputo. For the first problem, OHAM provides the exact solution, and for the second problem, it performs a highly accurate numerical approximation of the solution compare with the exact solution. The presented simulation results of OHAM comparison with analytical and numerical approaches reveal that the method is an efficient technique to simulate the solution of time-fractional types of Navier-Stokes equation. |
| format | Article |
| id | doaj-art-d72605c31618486980a4ec32bff04a69 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-d72605c31618486980a4ec32bff04a692025-02-03T01:24:59ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/55478045547804A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes EquationZeeshan Ali0Shayan Naseri Nia1Faranak Rabiei2Kamal Shah3Ming Kwang Tan4School of Engineering, Monash University Malaysia, 47500 Selangor, MalaysiaSchool of Engineering, Monash University Malaysia, 47500 Selangor, MalaysiaSchool of Engineering, Monash University Malaysia, 47500 Selangor, MalaysiaDepartment of Mathematics, University of Malakand, Dir(L), 18000 Khyber Pakhtunkhwa, PakistanSchool of Engineering, Monash University Malaysia, 47500 Selangor, MalaysiaIn this manuscript, a semianalytical solution of the time-fractional Navier-Stokes equation under Caputo fractional derivatives using Optimal Homotopy Asymptotic Method (OHAM) is proposed. The above-mentioned technique produces an accurate approximation of the desired solutions and hence is known as the semianalytical approach. The main advantage of OHAM is that it does not require any small perturbations, linearization, or discretization and many reductions of the computations. Here, the proposed approach’s reliability and efficiency are demonstrated by two applications of one-dimensional motion of a viscous fluid in a tube governed by the flow field by converting them to time-fractional Navier-Stokes equations in cylindrical coordinates using fractional derivatives in the sense of Caputo. For the first problem, OHAM provides the exact solution, and for the second problem, it performs a highly accurate numerical approximation of the solution compare with the exact solution. The presented simulation results of OHAM comparison with analytical and numerical approaches reveal that the method is an efficient technique to simulate the solution of time-fractional types of Navier-Stokes equation.http://dx.doi.org/10.1155/2021/5547804 |
| spellingShingle | Zeeshan Ali Shayan Naseri Nia Faranak Rabiei Kamal Shah Ming Kwang Tan A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation Advances in Mathematical Physics |
| title | A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation |
| title_full | A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation |
| title_fullStr | A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation |
| title_full_unstemmed | A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation |
| title_short | A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation |
| title_sort | semianalytical approach to the solution of time fractional navier stokes equation |
| url | http://dx.doi.org/10.1155/2021/5547804 |
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