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 inAlexandria engineering journal Vol. 61; no. 7; pp. 5753 - 5769
Main Authors Arqub, Omar Abu, Al-Smadi, Mohammed, Almusawa, Hassan, Baleanu, Dumitru, Hayat, Tasawar, Alhodaly, Mohammed, Osman, M.S.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2022
Elsevier
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Online AccessGet full text
ISSN1110-0168
DOI10.1016/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.
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
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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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