Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential Equations
In this work, we present a modified generalized Mittag–Leffler function method (MGMLFM) and Laplace Adomian decomposition method (LADM) to get an analytic-approximate solution for nonlinear systems of partial differential equations (PDEs) of fractional-order in the Caputo derivative. We apply the MG...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/1/32 |
| _version_ | 1797493913416630272 |
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| author | Hegagi Mohamed Ali Hijaz Ahmad Sameh Askar Ismail Gad Ameen |
| author_facet | Hegagi Mohamed Ali Hijaz Ahmad Sameh Askar Ismail Gad Ameen |
| author_sort | Hegagi Mohamed Ali |
| collection | DOAJ |
| description | In this work, we present a modified generalized Mittag–Leffler function method (MGMLFM) and Laplace Adomian decomposition method (LADM) to get an analytic-approximate solution for nonlinear systems of partial differential equations (PDEs) of fractional-order in the Caputo derivative. We apply the MGMLFM and LADM on systems of nonlinear time-fractional PDEs. Precisely, we consider some important fractional-order nonlinear systems, namely Broer–Kaup (BK) and Burgers, which have found major significance because they arise in many physical applications such as shock wave, wave processes, vorticity transport, dispersal in porous media, and hydrodynamic turbulence. The analysis of these methods is implemented on the BK, Burgers systems and solutions have been offered in a simple formula. We show our results in figures and tables to demonstrate the efficiency and reliability of the used methods. Furthermore, our outcome converges rapidly to the given exact solutions. |
| first_indexed | 2024-03-10T01:26:48Z |
| format | Article |
| id | doaj.art-6b8ff6fc50064535be5ad7d94ee8f04b |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T01:26:48Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-6b8ff6fc50064535be5ad7d94ee8f04b2023-11-23T13:48:57ZengMDPI AGFractal and Fractional2504-31102022-01-01613210.3390/fractalfract6010032Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential EquationsHegagi Mohamed Ali0Hijaz Ahmad1Sameh Askar2Ismail Gad Ameen3Department of Mathematics, Faculty of Science, Aswan University, Aswan 81528, EgyptSection of Mathematics, International Telematic University Uninettuno, 00186 Roma, ItalyDepartment of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, Faculty of Science, South Valley University, Qena 83523, EgyptIn this work, we present a modified generalized Mittag–Leffler function method (MGMLFM) and Laplace Adomian decomposition method (LADM) to get an analytic-approximate solution for nonlinear systems of partial differential equations (PDEs) of fractional-order in the Caputo derivative. We apply the MGMLFM and LADM on systems of nonlinear time-fractional PDEs. Precisely, we consider some important fractional-order nonlinear systems, namely Broer–Kaup (BK) and Burgers, which have found major significance because they arise in many physical applications such as shock wave, wave processes, vorticity transport, dispersal in porous media, and hydrodynamic turbulence. The analysis of these methods is implemented on the BK, Burgers systems and solutions have been offered in a simple formula. We show our results in figures and tables to demonstrate the efficiency and reliability of the used methods. Furthermore, our outcome converges rapidly to the given exact solutions.https://www.mdpi.com/2504-3110/6/1/32fractional partial differential equationsLaplace transformAdomian decomposition methodMittag–Leffler functionanalytic-approximate solutions |
| spellingShingle | Hegagi Mohamed Ali Hijaz Ahmad Sameh Askar Ismail Gad Ameen Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential Equations Fractal and Fractional fractional partial differential equations Laplace transform Adomian decomposition method Mittag–Leffler function analytic-approximate solutions |
| title | Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential Equations |
| title_full | Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential Equations |
| title_fullStr | Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential Equations |
| title_full_unstemmed | Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential Equations |
| title_short | Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential Equations |
| title_sort | efficient approaches for solving systems of nonlinear time fractional partial differential equations |
| topic | fractional partial differential equations Laplace transform Adomian decomposition method Mittag–Leffler function analytic-approximate solutions |
| url | https://www.mdpi.com/2504-3110/6/1/32 |
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