Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods
This work is reported the analytical solutions for describing the nonlinear directional couplers with metamaterials by including spatial–temporal fractional beta derivative evolution. The auxiliary ordinary differential equation method and the generalized Riccati method with the properties of beta d...
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2021-02-01
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doaj-7b4b1c06200c4e6a8f747ceabc867adc2021-06-02T15:22:09ZengElsevierAlexandria Engineering Journal1110-01682021-02-0160110551065Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methodsM.F. Uddin0M.G. Hafez1Z. Hammouch2H. Rezazadeh3D. Baleanu4Department of Mathematics, Chittagong University of Engineering and Technology, Chittagong 4349, BangladeshDepartment of Mathematics, Chittagong University of Engineering and Technology, Chittagong 4349, BangladeshDivision of Applied mathematics, Thu Dau Mot University Binh Duong Province, Viet Nam; Corresponding author.Amol University of Special Modern Technologies, Amol, IranCankaya University Ankara Turkey and Institute of Space Science Bucarest, Romania; China Medical University, Taichung, TaiwanThis work is reported the analytical solutions for describing the nonlinear directional couplers with metamaterials by including spatial–temporal fractional beta derivative evolution. The auxiliary ordinary differential equation method and the generalized Riccati method with the properties of beta derivative are implemented to secure such solutions. The solutions are obtained in the new forms by involving of some useful mathematical functions. The constraint conditions among the traveling wave parameters are evaluated. Some of the obtained solutions are presented graphically to illustrate the effectiveness of beta derivative parameter and mathematical techniques. It is investigated that the amplitudes of soliton are increased with the increase of fractional beta derivative parameter. The obtained results would be very useful to examine and understand the physical issues in nonlinear optics, especially in twin-core couplers with optical metamaterials.http://www.sciencedirect.com/science/article/pii/S1110016820305512Fractional Beta derivative evolutionNonlinear directional couplers with metamaterialsTraveling wave solutionsThe auxiliary ordinary differential equation methodThe generalized Riccati method |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
M.F. Uddin M.G. Hafez Z. Hammouch H. Rezazadeh D. Baleanu |
spellingShingle |
M.F. Uddin M.G. Hafez Z. Hammouch H. Rezazadeh D. Baleanu Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods Alexandria Engineering Journal Fractional Beta derivative evolution Nonlinear directional couplers with metamaterials Traveling wave solutions The auxiliary ordinary differential equation method The generalized Riccati method |
author_facet |
M.F. Uddin M.G. Hafez Z. Hammouch H. Rezazadeh D. Baleanu |
author_sort |
M.F. Uddin |
title |
Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods |
title_short |
Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods |
title_full |
Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods |
title_fullStr |
Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods |
title_full_unstemmed |
Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods |
title_sort |
traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods |
publisher |
Elsevier |
series |
Alexandria Engineering Journal |
issn |
1110-0168 |
publishDate |
2021-02-01 |
description |
This work is reported the analytical solutions for describing the nonlinear directional couplers with metamaterials by including spatial–temporal fractional beta derivative evolution. The auxiliary ordinary differential equation method and the generalized Riccati method with the properties of beta derivative are implemented to secure such solutions. The solutions are obtained in the new forms by involving of some useful mathematical functions. The constraint conditions among the traveling wave parameters are evaluated. Some of the obtained solutions are presented graphically to illustrate the effectiveness of beta derivative parameter and mathematical techniques. It is investigated that the amplitudes of soliton are increased with the increase of fractional beta derivative parameter. The obtained results would be very useful to examine and understand the physical issues in nonlinear optics, especially in twin-core couplers with optical metamaterials. |
topic |
Fractional Beta derivative evolution Nonlinear directional couplers with metamaterials Traveling wave solutions The auxiliary ordinary differential equation method The generalized Riccati method |
url |
http://www.sciencedirect.com/science/article/pii/S1110016820305512 |
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