Dynamical and sensitivity analysis for fractional Kundu–Eckhaus system to produce solitary wave solutions via new mapping approach

References

• Ahmad, M., Zada, A., Ghaderi, M., George, R., & Rezapour, S. (2022). On the existence and stability of a neutral stochastic fractional differential system. Fractal and Fractional, 6(4), 203. doi:10.3390/fractalfract6040203
   Web of Science ®Google Scholar
• Alabedalhadi, M., Al-Omari, S., Al-Smadi, M., & Alhazmi, S. (2023). Traveling wave solutions for time-fractional mKdV-ZK Equation of weakly nonlinear ion-acoustic waves in magnetized electron-positron plasma. Symmetry, 15(2), 361. doi:10.3390/sym15020361
   Google Scholar
• Alam, M. N., & Tunç, C. (2020a). New solitary wave structures to the (2 + 1)-dimensional KD and KP equations with spatio-temporal dispersion. Journal of King Saud University - Science, 32(8), 3400–3409. doi:10.1016/j.jksus.2020.09.027
   Web of Science ®Google Scholar
• Alam, M. N., & Tunç, C. (2020b). Constructions of the optical solitons and others soliton to the conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity. Journal of Taibah University for Science, 14(1), 94–100. doi:10.1080/16583655.2019.1708542
   Web of Science ®Google Scholar
• Almatrafi, M. B., Ragaa Alharbi, A., & Tunç, C. (2020). Constructions of the soliton solutions to the good Boussinesq equation. Advances in Difference Equations, 2020(1), 14. doi:10.1186/s13662-020-03089-8
   Web of Science ®Google Scholar
• Alam, M. N., Akash, H. S., Saha, U., Hasan, M. S., Parvin, W., & Tunç, C. (2023). Bifurcation analysis and solitary wave analysis of the nonlinear fractional soliton neuron model. Iranian Journal of Science, 47(5–6), 1797–1808. doi:10.1007/s40995-023-01555-y
   Google Scholar
• Alam, M. N., Iqbal, M., Hassan, M., Al-Asad, M. F., Hossain, M. S., & Tunç, C. (2024). Bifurcation, phase plane analysis and exact soliton solutions in the nonlinear Schrodinger equation with Atangana’s conformable derivative. Chaos, Solitons and Fractals, 182, 114724. doi:10.1016/j.chaos.2024.114724
   Web of Science ®Google Scholar
• Baleanu, D., Aydogn, S. M., Mohammadi, H., & Rezapour, S. (2020). On modelling of epidemic childhood diseases with the Caputo-Fabrizio derivative by using the Laplace Adomian decomposition method. Alexandria Engineering Journal, 59(5), 3029–3039. doi:10.1016/j.aej.2020.05.007
   Web of Science ®Google Scholar
• Baleanu, D., Jajarmi, A., Mohammadi, H., & Rezapour, S. (2020). A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative. Chaos, Solitons & Fractals, 134, 109705. doi:10.1016/j.chaos.2020.109705
   Web of Science ®Google Scholar
• Batool, A., Talib, I., Riaz, M. B., & Tunç, C. (2022). Extension of lower and upper solutions approach for generalized nonlinear fractional boundary value problems. Arab Journal of Basic and Applied Sciences, 29(1), 249–256. doi:10.1080/25765299.2022.2112646
   Google Scholar
• Chen, Y., & Wang, Q. (2005). Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to (1 + 1)-dimensional dispersive long wave equation. Chaos, Solitons and Fractals, 24(3), 745–757. doi:10.1016/j.chaos.2004.09.014
   Web of Science ®Google Scholar
• Das, N., & Saha Ray, S. (2022). Dispersive optical soliton wave solutions for the time-fractional perturbed nonlinear Schrödinger equation with truncated M-fractional conformable derivative in the nonlinear optical fibers. Optical and Quantum Electronics, 54, 544.
   Web of Science ®Google Scholar
• Das, N., & Saha Ray, S. (2023). Dispersive optical soliton solutions of the (2 + 1)-dimensional cascaded system governing by coupled nonlinear Schrödinger equation with Kerr law nonlinearity in plasma. Optical and Quantum Electronics, 55, 328.
   Web of Science ®Google Scholar
• Dehingia, K., Mohsen, A. A., Alharbi, S. A., Alsemiry, R. D., & Rezapour, S. (2022). Dynamical behavior of a fractional order model for within-host SARS-CoV-2. Mathematics, 10(13), 2344. doi:10.3390/math10132344
   Web of Science ®Google Scholar
• Filiz, A., Ekici, M., & Sonmezoglu, A. (2014). F-expansion method and new exact solution of the Schrödinger-KdV equation. The Scientific World Journal, 14, 534063.
   Google Scholar
• Ge, Z.-M., & Ou, C.-Y. (2008). Chaos synchronization of fractional order modified Duffing systems with parameters excited by a chaotic signal. Chaos, Solitons & Fractals, 35(4), 705–717. doi:10.1016/j.chaos.2006.05.101
   Web of Science ®Google Scholar
• Haque, M. A., Zakariya, M. A., Singh, N. S. S., Paul, L. C., & Ishraque, M. F. (2023). Investigation of coupling loss caused by misalignment in optical fiber. Bulletin of Electrical Engineering and Informatics, 12(3), 1560–1569. doi:10.11591/eei.v12i3.4552
   Google Scholar
• Jiao, M., He, J., He, C., & Alsolami, A. A. (2024). Variational principle for Schrödinger-KdV system with the M-fractional derivatives. Journal of Computational Applied Mechanics, 55(2), 235–241. doi:10.22059/jcamech.2024.374235.1012
   Web of Science ®Google Scholar
• Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65–70. doi:10.1016/j.cam.2014.01.002
   Web of Science ®Google Scholar
• Khan, H., Alam, K., Gulzar, H., Etemad, S., & Rezapour, S. (2022). A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations. Mathematics and Computers in Simulation, 198, 455–473. doi:10.1016/j.matcom.2022.03.009
   Web of Science ®Google Scholar
• Khater, M. M. A., Ghanbari, B., Nisar, K. S., & Kumar, D. (2020). Novel exact solutions of the fractional Bogoyavlensky-Konopelchenko equation involving the Atangana-Baleanu-Riemann derivative. Alexandria Engineering Journal, 59(5), 2957–2967. doi:10.1016/j.aej.2020.03.032
   Web of Science ®Google Scholar
• Liu, S., Fu, Z., Liu, S., & Zhao, Q. (2001). Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Physics Letters A, 289(1–2), 69–74. doi:10.1016/S0375-9601(01)00580-1
   Web of Science ®Google Scholar
• Lü, D. (2005). Jacobi elliptic function solutions for two variant Boussinesq equations. Chaos, Solitons and Fractals, 24(5), 1373–1385. doi:10.1016/j.chaos.2004.09.085
   Web of Science ®Google Scholar
• Mohammed, W. W., El-Morshedy, M., Moumen, A., Ali, E. E., Benaissa, M., & Abouelregal, A. E. (2023). Effects of M-truncated derivative and multiplicative noise on the exact solutions of the breaking soliton equation. Symmetry, 15(2), 288. doi:10.3390/sym15020288
   Google Scholar
• Naeem, M., Rezazadeh, H., Khammash, A. A., Shah, R., & Zaland, S. (2022). Analysis of the fuzzy fractional-order solitary wave solutions for the KdV equation in the sense of Caputo-Fabrizio derivative. Journal of Mathematics, 2022, 3688916.
   Web of Science ®Google Scholar
• Rabie, W. B., Ahmed, H. M., & Hamdy, W. (2023). Exploration of new optical solitons in magnetooptical waveguide with coupled system of nonlinear Biswas–Milovic equation via Kudryashovís law using extended F-expansion method. Mathematics, 11(2), 300. doi:10.3390/math11020300
   Web of Science ®Google Scholar
• Rafiq, M. N., Majeed, A., Inc, M., & Kamran, M. (2022). New traveling wave solutions for space-time fractional modified equal width equation with beta derivative. Physics Letters A, 446, 128281. doi:10.1016/j.physleta.2022.128281
   Web of Science ®Google Scholar
• Rahmatullah Ellahi, R., Mohyud-Din, S. T., & Khan, U. Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method. Results in Physics, 2018, 8, 114–120. doi:10.1016/j.rinp.2017.11.023
   Web of Science ®Google Scholar
• Riaz, M. B., Rehman, A. U., & Martinovic, J. (n.d.). Application of the new mapping method to complex three coupled Maccari’s system possessing M-fractional derivative. Chaos Theory and Applications, 6(3). doi:10.51537/chaos.1414782
   Google Scholar
• Saha Ray, S., & Das, N. (2022). New optical soliton solutions of fractional perturbed nonlinear Schrödinger equation in nanofibers. Modern Physics Letters B, 36(2), 2150544. doi:10.1142/S0217984921505448
   Google Scholar
• Senol, M. (2020). New analytical solutions of fractional symmetric regularized-long-wave equation. Revista Mexicana de Física, 66(3 May–Jun), 297–307. doi:10.31349/RevMexFis.66.297
   Web of Science ®Google Scholar
• Tuan, N. H., Mohammadi, H., & Rezapour, S. (2020). A mathematical model for COVID-19 transmission by using the Caputo fractional derivative. Chaos, Solitons, and Fractals, 140, 110107. doi:10.1016/j.chaos.2020.110107
   PubMed Web of Science ®Google Scholar
• Vanterler, J., Sousa, D. A. C., Capelas, E., & Oliveira, D. E. (2018). A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties. International Journal of Analysis and Applications, 16, 83–96.
   Google Scholar
• Vega-Guzman, J., Ullah, M. Z., Asma, M., Zhou, Q., & Biswas, A. (2017). Dispersive solitons in magneto-optic waveguides. Superlattices and Microstructures, 103, 161–170. doi:10.1016/j.spmi.2017.01.020
   Web of Science ®Google Scholar
• Wang, Y.-Y., Su, C.-Q., Liu, X.-Q., & Li, J.-G. (2018). Nonautonomous solitons for an extended forced Korteweg-de Vries equation with variable coefficients in the fluid or plasma. Waves in Random and Complex Media, 28(3), 411–425. doi:10.1080/17455030.2017.1356944
   Web of Science ®Google Scholar
• Zaslavsky, G. M. (2002). Chaos, fractional kinetics, and anomalous transport. Physics Reports, 371(6), 461–580. doi:10.1016/S0370-1573(02)00331-9
   Google Scholar
• Zayed, E. M.E., & Alurrfi, K. A.E. (2017). Solitons and other solutions for two nonlinear Schrödinger equations using the new mapping method. Optik, 144, 132–148. doi:10.1016/j.ijleo.2017.06.101
   Web of Science ®Google Scholar
• Zeng, X., & Yong, X. (2008). A new mapping method and its applications to nonlinear partial differential equations. Physics Letters A, 372(44), 6602–6607. doi:10.1016/j.physleta.2008.09.025
   Web of Science ®Google Scholar
• Zheng, B., & Feng, Q. (2014). The Jacobi elliptic equation method for solving fractional partial differential equations. Abstract and Applied Analysis, 2014, 9. http://dx.doi.org/10.1155/2014/249071
   Google Scholar
• Zhu, W., Ling, Z., Xia, Y., & Gao, M. (2023). Bifurcations and the exact solutions of the time-space fractional complex Ginzburg-Landau equation with parabolic law nonlinearity. Fractal and Fractional, 7(2), 201. doi:10.3390/fractalfract7020201
   Web of Science ®Google Scholar