Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
In this study, we introduce an efficient analysis of a new equation, termed the time-fractional qq-deformed tanh-Gordon equation (TGE), which is the fractional form of the qq-deformed TGE that was recently introduced by Ali and Alharbi. This equation represents a significant advancement in the field...
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-11-01
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| Series: | Open Physics |
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| Online Access: | https://doi.org/10.1515/phys-2024-0094 |
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| author | Ali Khalid K. Mohamed Mohamed S. Alharbi Weam G. Maneea Marwa |
| author_facet | Ali Khalid K. Mohamed Mohamed S. Alharbi Weam G. Maneea Marwa |
| author_sort | Ali Khalid K. |
| collection | DOAJ |
| description | In this study, we introduce an efficient analysis of a new equation, termed the time-fractional qq-deformed tanh-Gordon equation (TGE), which is the fractional form of the qq-deformed TGE that was recently introduced by Ali and Alharbi. This equation represents a significant advancement in the field of mathematical physics, which is due to its applications in many fields including superconductivity and fiber optics. It has many applications in condensed matter physics and in modeling physical systems that exhibit violated symmetries. We investigate the qq-deformed TGE in fractional form using Caputo fractional derivative to capture non-local and memory effects, which means they can take into account the entire history of a function rather than just its current value. Notably, this equation has not been previously solved in fractional form, making our approach pioneering in its analysis. We solve this equation utilizing the modified double Laplace transform method, which is considered a semi-analytical technique that combines the double Laplace transform with Adomian polynomials to enable us to extract nonlinear terms. This method renowned for its efficacy in handling fractional differential equations; this is evident from the results obtained in the tables by comparing the analytical solution with the approximate solution we obtained, as well as by calculating the absolute error between them. We examine the existence and the uniqueness of the solution utilizing Schaefer’s fixed-point theorem. Different graphs in 2D and 3D are presented to clarify the effect of different parameters on the behavior of the solution, specially the fractional operator and the deformation parameter qq. |
| format | Article |
| id | doaj-art-4d66c0b65e8048bcbb1bb15a75999b91 |
| institution | Kabale University |
| issn | 2391-5471 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Physics |
| spelling | doaj-art-4d66c0b65e8048bcbb1bb15a75999b912024-11-25T11:19:21ZengDe GruyterOpen Physics2391-54712024-11-0122171310.1515/phys-2024-0094Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform methodAli Khalid K.0Mohamed Mohamed S.1Alharbi Weam G.2Maneea Marwa3Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, EgyptDepartment of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, Tabuk, 71491, Saudi ArabiaFaculty of Engineering, MTI University, Cairo, EgyptIn this study, we introduce an efficient analysis of a new equation, termed the time-fractional qq-deformed tanh-Gordon equation (TGE), which is the fractional form of the qq-deformed TGE that was recently introduced by Ali and Alharbi. This equation represents a significant advancement in the field of mathematical physics, which is due to its applications in many fields including superconductivity and fiber optics. It has many applications in condensed matter physics and in modeling physical systems that exhibit violated symmetries. We investigate the qq-deformed TGE in fractional form using Caputo fractional derivative to capture non-local and memory effects, which means they can take into account the entire history of a function rather than just its current value. Notably, this equation has not been previously solved in fractional form, making our approach pioneering in its analysis. We solve this equation utilizing the modified double Laplace transform method, which is considered a semi-analytical technique that combines the double Laplace transform with Adomian polynomials to enable us to extract nonlinear terms. This method renowned for its efficacy in handling fractional differential equations; this is evident from the results obtained in the tables by comparing the analytical solution with the approximate solution we obtained, as well as by calculating the absolute error between them. We examine the existence and the uniqueness of the solution utilizing Schaefer’s fixed-point theorem. Different graphs in 2D and 3D are presented to clarify the effect of different parameters on the behavior of the solution, specially the fractional operator and the deformation parameter qq.https://doi.org/10.1515/phys-2024-0094fractional calculusq-deformed tanh-gordon equationdouble laplace transform methodadomian polynomialsschaefer’s fixed-point theoremexistence and uniqueness analysis |
| spellingShingle | Ali Khalid K. Mohamed Mohamed S. Alharbi Weam G. Maneea Marwa Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method Open Physics fractional calculus q-deformed tanh-gordon equation double laplace transform method adomian polynomials schaefer’s fixed-point theorem existence and uniqueness analysis |
| title | Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method |
| title_full | Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method |
| title_fullStr | Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method |
| title_full_unstemmed | Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method |
| title_short | Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method |
| title_sort | innovative analysis to the time fractional q deformed tanh gordon equation via modified double laplace transform method |
| topic | fractional calculus q-deformed tanh-gordon equation double laplace transform method adomian polynomials schaefer’s fixed-point theorem existence and uniqueness analysis |
| url | https://doi.org/10.1515/phys-2024-0094 |
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