Analytical analysis of fractional nonlinear Jaulent-Miodek system with energy-dependent Schrödinger potential
In this work, a novel technique is considered for analyzing the fractional-order Jaulent-Miodek system. The suggested approach is based on the use of the residual power series technique in conjunction with the Laplace transform and Caputo operator to solve the system of equations. The Caputo derivat...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2023-07-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2023.1148306/full |
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| author | Ma’mon Abu Hammad Albandari W. Alrowaily Rasool Shah Sherif M. E. Ismaeel Sherif M. E. Ismaeel Samir A. El-Tantawy Samir A. El-Tantawy |
| author_facet | Ma’mon Abu Hammad Albandari W. Alrowaily Rasool Shah Sherif M. E. Ismaeel Sherif M. E. Ismaeel Samir A. El-Tantawy Samir A. El-Tantawy |
| author_sort | Ma’mon Abu Hammad |
| collection | DOAJ |
| description | In this work, a novel technique is considered for analyzing the fractional-order Jaulent-Miodek system. The suggested approach is based on the use of the residual power series technique in conjunction with the Laplace transform and Caputo operator to solve the system of equations. The Caputo derivative is applied to express the fractional operator, which is more suitable for modeling real-world phenomena with memory effects. As a real example, the proposed technique is implemented for analyzing the Jaulent-Miodek equation under suitable initial conditions. Additionally, the proposed technique’s validity (accuracy and effectiveness) is examined by studying some numerical examples. The obtained solutions show that the suggested technique can provide a reliable solution for the fractional-order Jaulent-Miodek system, making it a helpful tool for researchers in different areas, including engineering, physics, and mathematics. We also analyze the absolute error between the derived approximations and the analytical solutions to check the validation and accuracy of the obtained approximations. Many researchers can benefit from both the obtained approximations and the suggested method in analyzing many complicated nonlinear systems in plasma physics and nonlinear optics, and many others. |
| first_indexed | 2024-03-13T00:32:44Z |
| format | Article |
| id | doaj.art-3749748961c74d83a7eeebab0530d4ad |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-03-13T00:32:44Z |
| publishDate | 2023-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-3749748961c74d83a7eeebab0530d4ad2023-07-10T09:46:39ZengFrontiers Media S.A.Frontiers in Physics2296-424X2023-07-011110.3389/fphy.2023.11483061148306Analytical analysis of fractional nonlinear Jaulent-Miodek system with energy-dependent Schrödinger potentialMa’mon Abu Hammad0Albandari W. Alrowaily1Rasool Shah2Sherif M. E. Ismaeel3Sherif M. E. Ismaeel4Samir A. El-Tantawy5Samir A. El-Tantawy6Department of Mathematics, Al-Zaytoonah University of Jordan, Amman, JordanDepartment of Physics, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi ArabiaDepartment of Mathematics, Abdul Wali Khan University Mardan, Mardan, PakistanDepartment of Physics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Riyadh, Saudi ArabiaDepartment of Physics, Faculty of Science, Ain Shams University, Cairo, EgyptDepartment of Physics, Faculty of Science, Port Said University, Port Said, EgyptResearch Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Baha University, Al Baha, Saudi ArabiaIn this work, a novel technique is considered for analyzing the fractional-order Jaulent-Miodek system. The suggested approach is based on the use of the residual power series technique in conjunction with the Laplace transform and Caputo operator to solve the system of equations. The Caputo derivative is applied to express the fractional operator, which is more suitable for modeling real-world phenomena with memory effects. As a real example, the proposed technique is implemented for analyzing the Jaulent-Miodek equation under suitable initial conditions. Additionally, the proposed technique’s validity (accuracy and effectiveness) is examined by studying some numerical examples. The obtained solutions show that the suggested technique can provide a reliable solution for the fractional-order Jaulent-Miodek system, making it a helpful tool for researchers in different areas, including engineering, physics, and mathematics. We also analyze the absolute error between the derived approximations and the analytical solutions to check the validation and accuracy of the obtained approximations. Many researchers can benefit from both the obtained approximations and the suggested method in analyzing many complicated nonlinear systems in plasma physics and nonlinear optics, and many others.https://www.frontiersin.org/articles/10.3389/fphy.2023.1148306/fullFractional-order Jaulent-Miodek systemResidual power seriesLaplace transformCaputo operatorFractional calculus |
| spellingShingle | Ma’mon Abu Hammad Albandari W. Alrowaily Rasool Shah Sherif M. E. Ismaeel Sherif M. E. Ismaeel Samir A. El-Tantawy Samir A. El-Tantawy Analytical analysis of fractional nonlinear Jaulent-Miodek system with energy-dependent Schrödinger potential Frontiers in Physics Fractional-order Jaulent-Miodek system Residual power series Laplace transform Caputo operator Fractional calculus |
| title | Analytical analysis of fractional nonlinear Jaulent-Miodek system with energy-dependent Schrödinger potential |
| title_full | Analytical analysis of fractional nonlinear Jaulent-Miodek system with energy-dependent Schrödinger potential |
| title_fullStr | Analytical analysis of fractional nonlinear Jaulent-Miodek system with energy-dependent Schrödinger potential |
| title_full_unstemmed | Analytical analysis of fractional nonlinear Jaulent-Miodek system with energy-dependent Schrödinger potential |
| title_short | Analytical analysis of fractional nonlinear Jaulent-Miodek system with energy-dependent Schrödinger potential |
| title_sort | analytical analysis of fractional nonlinear jaulent miodek system with energy dependent schrodinger potential |
| topic | Fractional-order Jaulent-Miodek system Residual power series Laplace transform Caputo operator Fractional calculus |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2023.1148306/full |
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