[1] Iomin, A.: Fractional evolution in quantum mechanics. Chaos, Solitons & Fractals: X 1, 100001 (2019). doi:10.1016/j.csfx.2018.100001
[2] Nasrolahpour, H.: Time fractional formalism: classical and quantum phenomena. arXiv preprint arXiv:1203.4515 (2012). doi:10.48550/arXiv.1203.4515
[3] Kumar, D., Baleanu, D.: Fractional calculus and its applications in physics. Frontiers Media SA (2019). doi:10.3389/fphy.2019.00081
[4] Faridi, W.A., Asjad, M.I., Jhangeer, A.: The fractional analysis of fusion and fssion process in plasma physics. Physica Scripta 96(10), 104008 (2021). doi:10.1088/1402-4896/ac0dfd
[5] Pandir, Y., Yildirim, A.: Analytical approach for the fractional differential equations by using the extended tanh method. Waves in Random and Complex Media 28(3), 399–410 (2018). doi:10.1080/17455030.2017.1356490
[6] Dubey, S., Chakraverty, S.: Application of modifed extended tanh method in solving fractional order coupled wave equations. Mathematics and Computers in Simulation 198, 509–520 (2022). doi:10.1016/j.matcom.2022.03.007
[7] Raslan, K., Ali, K.K., Shallal, M.A.: The modifed extended tanh method with the riccati equation for solving the space-time fractional ew and mew equations. Chaos, Solitons & Fractals 103, 404–409 (2017). doi:10.1016/j.chaos.2017.06.029
[8] Tuluce Demiray, S., Pandir, Y., Bulut, H.: Generalized kudryashov method for time-fractional differential equations. In: Abstract and Applied Analysis, vol. 2014, p. 901540 (2014). doi:10.1155/2014/901540
[9] Kumar, D., Seadawy, A.R., Joardar, A.K.: Modifed kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology. Chinese journal of physics 56(1), 75–85 (2018). doi:10.1016/j.cjph.2017.11.020
[10] Eslami, M., Sharif, A.: Extended hyperbolic method to the perturbed nonlinear chen–lee–liu equation with conformable derivative. Partial Differential Equations in Applied Mathematics 11, 100838 (2024). doi:10.1016/j.padiff.2024.100838
[11] Mohyud-Din, S.T., Bibi, S.: Exact solutions for nonlinear fractional differential equations using GG2′ -expansion method. Alexandria Engineering Journal 57(2), 1003–1008 (2018). doi:10.1016/j.aej.2017.01.035
[12] Al-Shawba, A.A., Abdullah, F.A., Azmi, A., Akbar, M.A.: An extension of the double (GG′ , G1 )- expansion method for conformable fractional differential equations. Complexity 2020(1), 7967328 (2020). doi:10.1155/2020/7967328
[13] Rezazadeh, H., Korkmaz, A., Eslami, M., Vahidi, J., Asghari, R.: Traveling wave solution of conformable fractional generalized reaction duffng model by generalized projective riccati equation method. Optical and Quantum Electronics 50, 1–13 (2018). doi:10.1007/s11082-018-1416-1
[14] Zheng, B., Wen, C.: Exact solutions for fractional partial differential equations by a new fractional subequation method. Advances in Difference Equations 2013, 1–12 (2013). doi:10.1186/1687-1847-2013-199
[15] Bekir, A., Güner, Ö., Cevikel, A.C.: Fractional complex transform and exp-function methods for fractional differential equations. In: Abstract and Applied Analysis, vol. 2013, p. 426462 (2013). doi:10.1155/2013/426462. Wiley Online Library
[16] Bekir, A., Güner, Ö., Ünsal, Ö.: The frst integral method for exact solutions of nonlinear fractional differential equations. Journal of Computational and Nonlinear Dynamics 10(2), 021020 (2015). doi:10.1115/1.4028065
[17] Baleanu, D., Jassim, H.K.: Exact solution of two-dimensional fractional partial differential equations. Fractal and Fractional 4(2), 21 (2020). doi:10.3390/fractalfract4020021
[18] Ghanbari, B., Inc, M.: A new generalized exponential rational function method to fnd exact special solutions for the resonance nonlinear schrödinger equation. The European Physical Journal Plus 133(4), 142 (2018). doi:10.1140/epjp/i2018-11984-1
[19] Ali, K.K., Yokus, A., Seadawy, A.R., Yilmazer, R.: The ion sound and langmuir waves dynamical system via computational modifed generalized exponential rational function. Chaos, Solitons & Fractals 161, 112381 (2022). doi:10.1016/j.chaos.2022.112381
[20] Aldhabani, M.S., Nonlaopon, K., Rezaei, S., Bayones, F.S., Elagan, S., El-Marouf, S.A.: Abundant solitary wave solutions to a perturbed schrödinger equation with kerr law nonlinearity via a novel approach. Results in Physics 35, 105385 (2022). doi:10.1016/j.rinp.2022.105385
[21] Nonlaopon, K., Günay, B., Mohamed, M.S., Elagan, S., Najati, S., Rezapour, S.: RETRACTED: On extracting new wave solutions to a modifed nonlinear Schrödinger’s equation using two integration methods. Elsevier (2022). doi:10.1016/j.rinp.2022.105589
[22] Peng, S.: Optical solutions of the generalized (2+ 1)-dimensional dynamical schrödinger equation using the generalized exponential rational function method. Journal of Applied Science and Engineering 27(1) (2023). doi:10.6180/jase.202401_27(1).0009
[23] Abbas, N., Hussain, A., Riaz, M.B., Ibrahim, T.F., Birkea, F.O., Tahir, R.A.: A discussion on the lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-kdv equation. Results in Physics 56, 107302 (2024). doi:10.1016/j.rinp.2023.107302
[24] Dhiman, S.K., Kumar, S.: Analyzing specifc waves and various dynamics of multi-peakons in (3+ 1)- dimensional p-type equation using a newly created methodology. Nonlinear Dynamics 112(12), 10277–10290 (2024). doi:10.1007/s11071-024-09588-7
[25] Sağlam Özkan, Y.: New exact solutions of the conformable space-time two-mode foam drainage equation by two effective methods. Nonlinear Dynamics 112(21), 19353–19369 (2024). doi:10.1007/s11071-024-10010-5
[26] Ulam, S.: Collected Papers of Enrico Fermi. University of Chicago Press, US (1965)
[27] Toda, M.: Theory of Nonlinear Lattices vol. 20. Springer, (2012)
[28] Ablowitz, M.J., Ladik, J.F.: Nonlinear differential- difference equations. Journal of Mathematical Physics 16(3), 598–603 (1975). doi:10.1063/1.522558
[29] Wadati, M.: Transformation theories for nonlinear discrete systems. Progress of Theoretical Physics Supplement 59, 36–63 (1976). doi:10.1143/PTPS.59.36
[30] Kevrekidis, P., Kevrekidis, I., Malomed, B.: Stability of solitary waves in fnite ablowitz–ladik lattices. Journal of Physics A: Mathematical and General 35(2), 267 (2002). doi:10.1088/0305-4470/35/2/307
[31] Hu, X.-B., Tam, H.-W.: Application of bilinear method to integrable differential-difference equations. Glasgow Mathematical Journal 43(A), 43–51 (2001). doi:10.1017/S0017089501000052
[32] Zhang, S., Dong, L., Ba, J.-M., Sun, Y.-N.: The (GG′ )-expansion method for nonlinear differentialdifference equations. Physics Letters A 373(10), 905–910 (2009)
[33] Bekir, A., Güner, Ö., Ayhan, B.: Exact solutions of some systems of fractional differential-difference equations. Mathematical Methods in the Applied Sciences 38(17), 3807–3817 (2015). doi:10.1002/mma.3318
[34] Arikoglu, A., Ozkol, I.: Solution of differential–difference equations by using differential transform method. Applied Mathematics and Computation 181(1), 153–162 (2006). doi:10.1016/j.amc.2006.01.022
[35] Zou, L., Wang, Z., Zong, Z.: Generalized differential transform method to differential-difference equation. Physics Letters A 373(45), 4142–4151 (2009). doi:10.1016/j.physleta.2009.09.036
[36] Feng, Q.-H.: Exact solutions for fractional differential-difference equations by an extended riccati sub-ode method. Communications in Theoretical Physics 59(5), 521 (2013). doi:10.1088/0253-6102/59/5/01
[37] Wu, G.-c., Lee, E.: Fractional variational iteration method and its application. Physics Letters A 374(25), 2506–2509 (2010). doi:10.1016/j.physleta.2010.04.034
[38] Narita, K.: New discrete modifed kdv equation. Progress of theoretical physics 86(4), 817–824 (1991). doi:10.1143/ptp/86.4.817