[1] E. Atilgan, M. Senol, A. Kurt, and O. Tasbozan, New wave solutions of time-fractional coupled Boussinesq-Whitham-Broer-Kaup equation as a model of water waves, China Ocean Eng., 33 (2019), 477–483.
[2] S. Q. Chen, M. H. Li, B. Guan, Y. Li, Y. Wang, X Lin, and T. Liu, Abundant variant wave patterns by coupled Boussinesq-Whitham-Broer-Kaup equations, Chinese J. Phys., 78 (2022), 485–494.
[3] V. Daftardar-Gejji and H. Jafari, Adomian decomposition: a tool for solving a system of fractional differential equations, J. Math. Anal. Appl., 301 (2005), 508–518.
[4] E. H. El Kinani and A. Ouhadan, Lie symmetry analysis of some time fractional partial differential equations, Int. J. Mod. Phys. Conf. Ser., 38 (2015), 1560075.
[5] Y. Q. Feng and J. C. Yu, Lie symmetry analysis of fractional ordinary differential equation with neutral delay, AIMS Mathematics, 6 (2021), 3592–3605.
[6] R. K. Gazizov and A. A. Kasatkin, Construction of exact solutions for fractional order differential equations by the invariant subspace method, Comput. Math. Appl., 66 (2013), 576–584.
[7] R. K. Gazizov, A. A. Kasatkin, and S. Y. Lukashchuk, Continuous transformation groups of fractional differential equations, Vestnik USATU, 9 (2007), 125–135.
[8] R. K. Gazizov, A. A. Kasatkin, and S. Y. Lukashchuk, Symmetry properties of fractional diffusion equations, Phys. Scr., T136 (2009), 014016.
[9] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
[10] N. H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, Volume 1, CRC Press, 1993.
[11] N. H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, Volume 2, CRC Press, 1994.
[12] N. H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, Volume 3, CRC Press, 1995.
[13] N. H. Ibragimov, A new conservation theorem, J. Math. Anal. Appl., 333 (2007), 311–328.
[14] N. H. Ibragimov, Nonlinear self-adjointness and conservation laws, J. Phys. A-Math. Theor., 44 (2011), 432002.
[15] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, New York, 2006.
[16] M. M. Meerschaert, H. P. Scheffler, and C. Tadjeran, Finite difference methods for two-dimensional fractional dispersion equation, J. Comput. Phys., 211 (2006), 249–261.
[17] S. Momani and Z. Odibat, Homotopy perturbation method for nonlinear partial differential equations of fractional order, Phys. Lett. A, 365 (2007), 345–350.
[18] S. Momani and Z. Odibat, Numerical comparison of methods for solving linear differential equations of fractional order, Chaos Solitons Fractals, 31 (2007), 1248–1255.
[19] A. M. Nass, Symmetry analysis of space-time fractional Poisson equation with a delay, Quaest. Math., 42 (2019), 1221–1235.
[20] P. J. Olver, Applications of Lie Groups to Differential Equations, Heidelberg: Springer, 1986.
[21] L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, 1982.
[22] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
[23] R. L. Sachs, On the integrable variant of the Boussinesq system: Painleve property rational solutions, a related many-body system, and equivalence with the AKNS hierarchy, Physica D, 30 (1988), 1–27.
[24] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, Yverdon, 1993.
[25] M. Yourdkhany and M. Nadjafikhah, Symmetries, similarity invariant solution, conservation laws and exact solutions of the time-fractional Harmonic Oscillator equation, J. Geom. Phys., 153 (2020), 103661.
[26] J. C. Yu, Lie symmetry analysis of time fractional Burgers equation, Korteweg-de Vries equation and generalized reaction-diffusion equation with delays, Int. J. Geom. Meth. Mod. Phys., 19 (2022), 2250219.
[27] J. C. Yu, Lie symmetry, exact solutions and conservation laws of time fractional Black–Scholes equation derived by the fractional Brownian motion, J. Appl. Anal., 30 (2024), 137–145.
[28] J. C. Yu and Y. Q. Feng, Lie symmetry analysis and exact solutions of space-time fractional cubic Schr¨odinger equation, Int. J. Geom. Meth. Mod. Phys., 19 (2022), 2250077.
[29] J. C. Yu and Y. Q. Feng, Lie symmetry, exact solutions and conservation laws of some fractional partial differential equations, J. Appl. Anal. Comput., 13 (2023), 1872–1889.
[30] J. C. Yu and Y. Q. Feng, Group classification of time fractional Black-Scholes equation with time-dependent coefficients, Fract. Calc. Appl. Anal., 27 (2024), 2335–2358.
[31] J. C. Yu and Y. Q. Feng, Lie symmetry analysis, power series solutions and conservation laws of (2+1)-dimensional time fractional modified Bogoyavlenskii–Schiff equations, J. Nonlinear Math. Phys., 31 (2024), 27.
[32] J. C. Yu and Y. Q. Feng, Lie symmetries, exact solutions and conservation laws of time fractional Boussinesq-Burgers system in ocean waves, Commun. Theor. Phys., 76 (2024), 125002.
[33] J. C. Yu and Y. Q. Feng, On the generalized time fractional reaction–diffusion equation: Lie symmetries, exact solutions and conservation laws, Chaos Solitons Fractals, 182 (2024), 114855.
[34] J. C. Yu and Y. Q. Feng, Symmetry analysis, optimal system, conservation laws and exact solutions of time fractional diffusion-type equation, Int. J. Geom. Meth. Mod. Phys., Online Ready, (2024), 2450286.
[35] J. C. Yu, Y. Q. Feng, and X. J. Wang, Lie symmetry analysis and exact solutions of time fractional Black-Scholes equation, Int. J. Financ. Eng., 9 (2022), 2250023.
[36] Z. Y. Zhang, Symmetry determination and nonlinearization of a nonlinear time-fractional partial differential equation, Proc. R. Soc. A, 476 (2020), 20190564.
[37] Z. Y. Zhang and G. F. Li, Lie symmetry analysis and exact solutions of the time-fractional biological population model, Phys. A, 540 (2020), 123134.
[38] S. Zhang and H. Q. Zhang, Fractional sub-equation method and its applications to nonlinear fractional PDEs, Phys. Lett. A, 375 (2011), 1069–1073.