A novel analytical algorithm for generalized fifth-order time-fractional nonlinear evolution equations with conformable time derivative arising in shallow water waves
The purpose of this research is to study, investigate, and analyze a class of temporal time-FNEE models with time-FCDs that are indispensable in numerous nonlinear wave propagation phenomena. For this purpose, an efficient semi-analytical algorithm is developed and designed in view of the residual e...
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Published in | Alexandria engineering journal Vol. 61; no. 7; pp. 5753 - 5769 |
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Main Authors | , , , , , , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
01.07.2022
Elsevier |
Subjects | |
Online Access | Get full text |
ISSN | 1110-0168 |
DOI | 10.1016/j.aej.2021.12.044 |
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Abstract | The purpose of this research is to study, investigate, and analyze a class of temporal time-FNEE models with time-FCDs that are indispensable in numerous nonlinear wave propagation phenomena. For this purpose, an efficient semi-analytical algorithm is developed and designed in view of the residual error terms for solving a class of fifth-order time-FCKdVEs. The analytical solutions of a dynamic wavefunction of the fractional Ito, Sawada-Kotera, Lax’s Korteweg-de Vries, Caudrey-Dodd-Gibbon, and Kaup-Kupershmidt equations are provided in the form of a convergent conformable time-fractional series. The related consequences are discussed both theoretically as well as numerically considering the conformable sense. In this direction, convergence analysis and error estimates of the developed algorithm are studied and analyzed as well. Concerning the considered models, specific unidirectional physical experiments are given in a finite compact regime to confirm the theoretical aspects and to demonstrate the superiority of the novel algorithm compared to the other existing numerical methods. Moreover, some representative results are presented in two- and three-dimensional graphs, whilst dynamic behaviors of fractional parameters are reported for several α values. From the practical viewpoint, the archived simulations and consequences justify that the iterative algorithm is a straightforward and appropriate tool with computational efficiency for long-wavelength solutions of nonlinear time-FPDEs in physical phenomena. |
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AbstractList | The purpose of this research is to study, investigate, and analyze a class of temporal time-FNEE models with time-FCDs that are indispensable in numerous nonlinear wave propagation phenomena. For this purpose, an efficient semi-analytical algorithm is developed and designed in view of the residual error terms for solving a class of fifth-order time-FCKdVEs. The analytical solutions of a dynamic wavefunction of the fractional Ito, Sawada-Kotera, Lax’s Korteweg-de Vries, Caudrey-Dodd-Gibbon, and Kaup-Kupershmidt equations are provided in the form of a convergent conformable time-fractional series. The related consequences are discussed both theoretically as well as numerically considering the conformable sense. In this direction, convergence analysis and error estimates of the developed algorithm are studied and analyzed as well. Concerning the considered models, specific unidirectional physical experiments are given in a finite compact regime to confirm the theoretical aspects and to demonstrate the superiority of the novel algorithm compared to the other existing numerical methods. Moreover, some representative results are presented in two- and three-dimensional graphs, whilst dynamic behaviors of fractional parameters are reported for several α values. From the practical viewpoint, the archived simulations and consequences justify that the iterative algorithm is a straightforward and appropriate tool with computational efficiency for long-wavelength solutions of nonlinear time-FPDEs in physical phenomena. |
Author | Almusawa, Hassan Alhodaly, Mohammed Al-Smadi, Mohammed Baleanu, Dumitru Osman, M.S. Arqub, Omar Abu Hayat, Tasawar |
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Keywords | FCRPSA OHAM FCKdVE HPM FCD Fractional conformable residual power series algorithm FNEE Fractional nonlinear evolution equation ADM FPDE Fractional conformable derivative LMM Fractional conformable Korteweg-de Vries equations MTFS Shallow water surfaces q-HAM VIM BPM |
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SubjectTerms | Fractional conformable derivative Fractional conformable Korteweg-de Vries equations Fractional conformable residual power series algorithm Fractional nonlinear evolution equation Shallow water surfaces |
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Title | A novel analytical algorithm for generalized fifth-order time-fractional nonlinear evolution equations with conformable time derivative arising in shallow water waves |
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