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Fractal Fract
Volume 9
Issue 11
10.3390/fractalfract9110720
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Fractional Optical Solitons in Metamaterial-Based Couplers with Strong Dispersion and Parabolic Nonlinearity

by
Karim K. Ahmed
1,
Hamdy M. Ahmed
2,
Taha Radwan
3,*,
M. Elsaid Ramadan
4,
Soliman Alkhatib
5 and
Mohammed H. Ali
6
1
Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo 11835, Egypt
2
Department of Mathematics and Engineering Physics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City 11837, Egypt
3
Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
4
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina 42351, Saudi Arabia
5
College of Engineering and Technology (CET), American University in the Emirates (AUE), Dubai Intel Academic City, Dubai P.O. Box 503000, United Arab Emirates
6
Department of Basic Science, Higher Institute of Computer Science and Information Systems, Fifth Settlement, Cairo 11835, Egypt
*
Author to whom correspondence should be addressed.
Fractal Fract. 2025, 9(11), 720; https://doi.org/10.3390/fractalfract9110720 (registering DOI)
Submission received: 23 September 2025 / Revised: 1 November 2025 / Accepted: 5 November 2025 / Published: 7 November 2025
(This article belongs to the Special Issue Recent Trends in Computational Physics with Fractional Applications)
Versions Notes

Abstract

The current study examines optical soliton solutions in a complicated system of metamaterial-based optical solutions coupled with extremely dispersive couplers. The conformable fractional derivative (CFD) influences the nonlinear refractive index, which is governed by a parabolic equation. Some soliton solutions are extracted, like bright, singular solitons, and singular periodic ones; also, Weierstrass elliptic doubly periodic, and several other exact solutions are systematically revealed by the study using the modified extended direct algebraic method. The findings shed important light on the many solitons in these intricate systems and the interactions between nonlinearity, dispersion, and metamaterial properties. The findings have significance beyond advancing our theoretical understanding of soliton behavior in metamaterial-based optical couplers; they might influence the advancement and development of optical communication technologies and systems. Complementary 2D and 3D representations show how stability parameters change throughout various dynamical regimes and confirm solution consistency. In order to comprehend the complex nonlinear phenomena of this system and its possible practical applications, this paper offers a comprehensive theoretical framework.
Keywords: metamaterial; highly dispersive couplers; modified extended direct algebraic technique; fractional derivatives; solitons; optical fiber metamaterial; highly dispersive couplers; modified extended direct algebraic technique; fractional derivatives; solitons; optical fiber

Share and Cite

MDPI and ACS Style

Ahmed, K.K.; Ahmed, H.M.; Radwan, T.; Ramadan, M.E.; Alkhatib, S.; Ali, M.H. Fractional Optical Solitons in Metamaterial-Based Couplers with Strong Dispersion and Parabolic Nonlinearity. Fractal Fract. 2025, 9, 720. https://doi.org/10.3390/fractalfract9110720

AMA Style

Ahmed KK, Ahmed HM, Radwan T, Ramadan ME, Alkhatib S, Ali MH. Fractional Optical Solitons in Metamaterial-Based Couplers with Strong Dispersion and Parabolic Nonlinearity. Fractal and Fractional. 2025; 9(11):720. https://doi.org/10.3390/fractalfract9110720

Chicago/Turabian Style

Ahmed, Karim K., Hamdy M. Ahmed, Taha Radwan, M. Elsaid Ramadan, Soliman Alkhatib, and Mohammed H. Ali. 2025. "Fractional Optical Solitons in Metamaterial-Based Couplers with Strong Dispersion and Parabolic Nonlinearity" Fractal and Fractional 9, no. 11: 720. https://doi.org/10.3390/fractalfract9110720

APA Style

Ahmed, K. K., Ahmed, H. M., Radwan, T., Ramadan, M. E., Alkhatib, S., & Ali, M. H. (2025). Fractional Optical Solitons in Metamaterial-Based Couplers with Strong Dispersion and Parabolic Nonlinearity. Fractal and Fractional, 9(11), 720. https://doi.org/10.3390/fractalfract9110720

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