Lie analysis and laws of conservation for the two-dimensional model of Newell–Whitehead–Segel regarding the Riemann operator fractional scheme in a time-independent variable

References

• Abu Arqub, O. (2019). Application of residual power series method for the solution of time-fractional Schrödinger equations in one-dimensional space. Fundamenta Informaticae, 166(2), 87–110. doi:10.3233/FI-2019-1795
   Web of Science ®Google Scholar
• Al-Deiakeh, R., Abu Arqub, O., Al-Smadi, M., & Momani, S. (2021). Lie symmetry analysis, explicit solutions, and conservation laws of the time-fractional Fisher equation in two-dimensional space. Journal of Ocean Engineering and Science, 2021, 1–8.
   Google Scholar
• Az-Zo’bi, E., Al-Maaitah, A. F., Tashtoush, M. A., & Osman, M. S. (2022). New generalised cubic–quintic–septic NLSE and its optical solitons. Pramana, 96(4), 184. doi:10.1007/s12043-022-02427-7
   Web of Science ®Google Scholar
• Bluman, G., & Kumei, S. (1989). Symmetries and differential equation. USA: Springer.
   Google Scholar
• Chen, S., & Ren, Y. (2022). Small amplitude periodic solution of Hopf bifurcation theorem for fractional differential equations of balance point in group competitive martial arts. Applied Mathematics and Nonlinear Sciences, 7(1), 207–214. doi:10.2478/amns.2021.2.00152
   Google Scholar
• Gao, J., Alotaibi, F. S., & Ismail, R. I. (2022). The model of sugar metabolism and exercise energy expenditure based on fractional linear regression equation. Applied Mathematics and Nonlinear Sciences, 7(1), 123–132. doi:10.2478/amns.2021.2.00026
   Google Scholar
• Gazizov, R. K., Ibragimov, N. H., & Lukashchuk, S. (2015). Conservation laws for time-fractional subdiffusion and diffusion-wave equations. Nonlinear Dynamics, 23(1–3), 153–163. doi:10.1016/j.cnsns.2014.11.010
   Google Scholar
• Goswami, A., Singh, J., Kumar, D., Gupta., & S., Sushila. (2019). An efficient analytical technique for fractional partial differential equations occurring in ion acoustic waves in plasma. Journal of Ocean Engineering and Science, 4(2), 85–99. doi:10.1016/j.joes.2019.01.003
   Web of Science ®Google Scholar
• Haque, M. M., Akbar, M. A., & Osman, M. S. (2022). Optical soliton solutions to the fractional nonlinear Fokas–Lenells and paraxial Schrödinger equations. Optical and Quantum Electronics, 54(11)volume, 764. doi:10.1007/s11082-022-04145-1
   Web of Science ®Google Scholar
• Khater, M. M. A., Attia, R. A. M., & Lu, D. (2019). Numerical solutions of nonlinear fractional Wu–Zhang system for water surface versus three approximate schemes. Journal of Ocean Engineering and Science, 4(2), 144–148. doi:10.1016/j.joes.2019.03.002
   Web of Science ®Google Scholar
• Kilbas, A., Srivastava, H., & Trujillo, J. (2006). Theory and applications of fractional differential equations. Netherlands: Elsevier.
   Google Scholar
• Kumar, D., & Sharma, R. P. (2016). Numerical approximation of Newell–Whitehead–Segel equation of fractional order. Nonlinear Engineering, 5(2), 81–86. doi:10.1515/nleng-2015-0032
   Google Scholar
• Kurt, A., Rezazadeh, H., Senol, M., Neirameh, A., Tasbozan, O., Eslami, M., & Mirzazadeh, M. (2019). Two effective approaches for solving fractional generalized Hirota-Satsuma coupled KdV system arising in interaction of long waves. Journal of Ocean Engineering and Science, 4(1), 24–32. doi:10.1016/j.joes.2018.12.004
   Web of Science ®Google Scholar
• Li, Y. (2022). Fractional differential equations in national sports training in colleges and universities. Applied Mathematics and Nonlinear Sciences, 7(1), 379–386. doi:10.2478/amns.2021.2.00158
   Google Scholar
• Liu, C. (2022). Precision algorithms in second-order fractional differential equations. Applied Mathematics and Nonlinear Sciences, 7(1), 155–164. doi:10.2478/amns.2021.2.00157
   Google Scholar
• Macias-Diaz, J. E., & Ruiz-Ramirez, J. (2011). A non-standard symmetry-preserving method to compute bounded solutions of a generalized Newell-Whitehead-Segel equation. Applied Numerical Mathematics, 61(4), 630–640. doi:10.1016/j.apnum.2010.12.008
   Web of Science ®Google Scholar
• Mainardi, F. (2010). Fractional calculus and waves in linear viscoelasticity. UK: Imperial College Press.
   Google Scholar
• Mangoub, M. M. A., & Sedeeg, A. K. H. (2016). On the solution of Newell–Whitehead–Segel equation. American Journal of Mathematical and Computer Modelling, 1, 21–24.
   Google Scholar
• Newell, A., & Whitehead, J. (1969). Finite bandwidth finite amplitude convection. Journal of Fluid Mechanics, 38(2), 279–303. doi:10.1017/S0022112069000176
   Google Scholar
• Nisar, K. S., Ilhan, O. A., Abdulazeez, S. T., Manafian, J., Mohammed, S. A., & Osman, M. S. (2021). Novel multiple soliton solutions for some nonlinear PDEs via multiple Exp-function method. Results in Physics, 21, 103769. doi:10.1016/j.rinp.2020.103769
   Web of Science ®Google Scholar
• Olver, P. J. (1993). Applications of lie groups to differential equations. USA: Springer.
   Google Scholar
• Osman, M. S., Tariq, K. U., Bekir, A., Elmoasry, A., Elazab, N. S., Younis, M., & Abdel-Aty, M. (2020). Investigation of soliton solutions with different wave structures to the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation. Communications in Theoretical Physics, 72(3), 35002. doi:10.1088/1572-9494/ab6181
   Web of Science ®Google Scholar
• Park, C., Nuruddeen, R. I., Ali, K. K., Muhammad, L., Osman, M. S., & Baleanu, D. (2020). Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations. Advances in Difference Equations, 2020(1), 627. doi:10.1186/s13662-020-03087-w
   Google Scholar
• Podlubny, I. (1999). Fractional differential equations. USA: Academic Press.
   Google Scholar
• Prakash, A., Goyal, M., & Gupta, S. (2019). Fractional variational iteration method for solving time-fractional Newell-Whitehead-Segel equation. Nonlinear Engineering, 8(1), 164–171. doi:10.1515/nleng-2018-0001
   Google Scholar
• Saravanan, A., & Magesh, N. (2013). A comparison between the reduced differential transform method and the Adomian decomposition method for the Newell-Whitehead-Segel equation. Journal of the Egyptian Mathematical Society, 21(3), 259–265. doi:10.1016/j.joems.2013.03.004
   Google Scholar
• Wang, G. W., Liu, X. Q., & Zhang, Y. Y. (2013a). Lie symmetry analysis to the time fractional generalized fifth-order KdV equation. Communications in Nonlinear Science and Numerical Simulation, 18(9), 2321–2326. doi:10.1016/j.cnsns.2012.11.032
   Web of Science ®Google Scholar
• Wang, W., Han, B., & Yamamoto, M. (2013b). Inverse heat problem of determining time-dependent source parameter in reproducing kernel space. Nonlinear Analysis: Real World Applications, 14(1), 875–887. doi:10.1016/j.nonrwa.2012.08.009
   Web of Science ®Google Scholar
• Wen, L., Liu, H., Chen, J., Fakieh, B., & Shorman, S. M. (2022). Fractional linear regression equation in agricultural disaster assessment model based on geographic information system analysis technology. Applied Mathematics and Nonlinear Sciences, 7(1), 275–284. doi:10.2478/amns.2021.2.00096
   Google Scholar
• Yang, H. W., Guo, M., & He, H. (2019). Conservation laws of space-time fractional mZK equation for Rossby solitary waves with complete Coriolis force. International Journal of Nonlinear Sciences and Numerical Simulation, 20(1), 17–32. doi:10.1515/ijnsns-2018-0026
   Web of Science ®Google Scholar
• Yao, S. W., Islam, M. E., Akbar, M. A., Inc, M., Adel, M., & Osman, M. S. (2022). Analysis of parametric effects in the wave profile of the variant Boussinesq equation through two analytical approaches. Open Physics, 20(1), 778–794. doi:10.1515/phys-2022-0071
   Web of Science ®Google Scholar
• Zaslavsky, G. M. (2005). Hamiltonian chaos and fractional dynamics. UK: Oxford University Press.
   Google Scholar
• Zhirong, G., & Alghazzawi, D. M. (2022). Optimal solution of fractional differential equations in solving the relief of college students’ mental obstacles. Applied Mathematics and Nonlinear Sciences, 7(1), 353–360. doi:10.2478/amns.2021.1.00095
   Google Scholar