Exact solutions of beta-fractional Fokas–Lenells equation via sine-cosine method
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 16 (2023) no. 2, pp. 5-13 Cet article a éte moissonné depuis la source Math-Net.Ru

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In nonlinear plasma physics, photonics and optics, the space-time fractional nonlinear Fokas–Lenells equation associated with beta derivative has significiant applications. This equation is used in this study to provide precise solutions using the Sine-Cosine method. Furthermore, using computer software, we plot the 2D-3D figures of the obtained solutions based on the appropriate parameters. The findings indicate that the suggested technique is simple, efficient and capable of producing complete solutions to nonlinear models due to mathematical physics.
Keywords: Sine-cosine method, beta derivative
Mots-clés : exact solutions, Fokas–Lenells equation.
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     title = {Exact solutions of beta-fractional {Fokas{\textendash}Lenells} equation via sine-cosine method},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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Volkan Ala; Berik Rakhimzhanov. Exact solutions of beta-fractional Fokas–Lenells equation via sine-cosine method. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 16 (2023) no. 2, pp. 5-13. http://geodesic.mathdoc.fr/item/VYURU_2023_16_2_a0/

[1] Adomian G., “A Review of the Decomposition Method and Some Recent Results for Nonlinear Equations”, Computers and Mathematics with Applications, 21:5 (1991), 101–127 | DOI | MR | Zbl

[2] Rezazadeh H., “New Solitons Solutions of the Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity”, Optik – International Journal for Light and Electron Optics, 167 (2018), 218–227 | DOI

[3] Tala-Tebue E., Tsobgni-Fozap D.C., Kenfack-Jiotsa A., Kofane T.C., “Envelope Periodic Solutions for a Discrete Network with the Jacobi Elliptic Functions and the Alternative $(G^{\prime}/G)$-Expansion Method Including the Generalized Riccati Equation”, European Physical Journal Plus, 129:6 (2014), 136, 10 pp. | DOI

[4] Bekova G., Yesmakhanova K., Ozat N., Shaikhova G., “Dark and Bright Solitons for the Two-Dimensional Complex Modified Korteweg–de Vries and Maxwell–Bloch System with Time-Dependent Coefficient” (Prague), Journal of Physics: Conference Series, 96 (2018), 012035, 10 pp.

[5] Yesmakhanova K., Bekova G., Shaikhova G., Myrzakulov R., “Soliton Solutions of the (2+1)-Dimensional Complex Modified Korteweg–de Vries and Maxwell–Bloch Equations” (Athens), Journal of Physics: Conference Series, 738 (2016), 012018, 7 pp. | DOI

[6] Harivan R.N., Ismael H.F., Nehad A.S., Wajaree W., “W-Shaped Soliton Solutions to the Modified Zakharov–Kuznetsov Equation of Ion-Acoustic Waves in (3+1)-Dimensions Arise in a Magnetized Plasma”, AIMS Mathematics, 8:2 (2023), 4467–4486 | DOI | MR

[7] Baskonus H.M., Bulut H., “Exponential Prototype Structures for (2+1)-Dimensional Boiti–Leon–Pempinelli Systems in Mathematical Physics”, Waves in Random and Complex Media, 26:2 (2016), 189–196 | DOI | MR | Zbl

[8] Mamedov Kh.R., Demirbilek U., Ala V., “Exact Solutions of the (2+1)-Dimensional Kundu–Mukherjee–Naskar Model via IBSEFM”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 15:2 (2022), 17–26 | DOI | MR | Zbl

[9] Burdik C., Shaikhova G., Rakhimzhanov B., “Soliton Solutions and Travelling Wave Solutions for the Two-Dimensional Generalized Nonlinear Schrödinger Equations”, European Physical Journal, 136:1095 (2021), 1–17 | DOI

[10] Shaikhova G., Kutum B., Myrzakulov R., “Periodic Traveling Wave, Bright and Dark Soliton Solutions of the (2+1)-Dimensional Complex Modified Korteweg–de Vries System of Equations by Using Three Different Methods”, AIMS Mathematics, 7:10 (2022), 18948–18970 | DOI | MR

[11] Ala V., Shaikhova G., “Analytical Solutions of Nonlinear Beta Fractional Schrödinger Equation via Sine-Cosine Method”, Lobachevskii Journal of Mathematics, 43:11 (2022), 3033–3038 | DOI | MR

[12] Yesmakhanova K., Shaikhova G., Bekova G., “Soliton Solutions of the Hirota's System” (Almaty), AIP Conference Proceedings, 1759 (2016), 020147, 5 pp. | DOI

[13] El-Wakil S.A., Abdou M.A., “New Exact Travelling Wave Solutions of Two Nonlinear Physical Models”, Nonlinear Analysis, 68:2 (2008), 235–245 | DOI | MR | Zbl

[14] Zafar A., Raheel M., Bekir A., Razzaq W., “The Conformable Space-Time Fractional Fokas–Lenells Equation and Its Optical Soliton Solutions Based on Three Analytical Schemes”, International Journal of Modern Physics B, 35:1 (2021), 2150004, 16 pp. | DOI | MR | Zbl

[15] Biswas A., Ekici M., Sonmezoglu A., Alqahtani R.T., “Optical Soliton Perturbation with Full Nonlinearity in Polarization Preserving Fibers Using Trial Equation Method”, Journal of Optoelectronics and Advanced Materials, 20:7–8 (2018), 385–402

[16] Biswas A., Yildirim Y., Yasar E., Triki H., Zhou Q., Moshokoa S.P., Belic M., “Optical Solitons with Differential Group Delay for Coupled Fokas–Lenells Equation by Extended Trial Function Scheme”, Optik – International Journal for Light and Electron Optics, 165 (2018), 102–110 | DOI | MR

[17] Demiray S.T., Bulut H., “New Exact Solutions of the New Hamiltonian Amplitude-Equation and Fokas–Lenells Equation”, Entropy, 17:9 (2015), 6025–6043 | DOI | MR | Zbl

[18] Ben-Hai Wang, Yue-Yue Wang, Chao-Qing Dai, Yi-Xiang Chen, “Dynamical Characteristic of Analytical Fractional Solitons for the Space-Time Fractional Fokas–Lenells Equation”, Alexandria Engineering Journal, 59:6 (2020), 4699–4707 | DOI

[19] Sajid N., Akram G., “Optical Solitons with Full Nonlinearity for the Conformable Space-Time Fractional Fokas–Lenells Equation”, Optik – International Journal for Light and Electron Optics, 196 (2019), 163131, 13 pp. | DOI

[20] Bulut H., Sulaiman T.A., Baskonus H.M., Rezazadeh H., Eslami M., Mirzazadeh M., “Optical Solitons and Other Solutions to the Conformable Space-Time Fractional Fokas–Lenells Equation”, Optik – International Journal for Light and Electron Optics, 172 (2018), 20–27 | DOI

[21] Sajid N., Akram G., “Dark, Singular, Bright, Rational and Periodic Solutions of the Space-Time Fractional Fokas–Lenells Equation by the $\phi^6$-Model Expansion”, Optik – International Journal for Light and Electron Optics, 228 (1658), 43, 26 pp. | DOI

[22] Morshedul Haque Md., Akbar M.A., Osman M.S., “Optical Soliton Solutions to the Fractional Nonlinear Fokas–Lenells and Paraxial Schrödinger Equations”, Optical and Quantum Electronics, 54 (2022), 517 | DOI

[23] Atangana A., Baleanu D., “New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model”, The Journal Thermal Science, 20 (2016), 763–769 | DOI

[24] Wazwaz A.M., “The Sine-Cosine Method for Obtaining Solutions with Compact and Noncompact Structures”, Applied Mathematics and Computation, 159:2 (2004), 559–576 | DOI | MR | Zbl

[25] Pashayi S., Hashemi M.S., Shahmorad S., “Analytical Lie Group Approach for Solving Fractional Integro Differential Equations”, Communications in Nonlinear Science and Numerical Simulation, 51 (2017), 66–77 | DOI | MR | Zbl