[1] Abazari, R., Jamshidzadeh, S. and Wang, G. Mathematical modeling of DNA vibrational dynamics and its solitary wave solutions, Rev. Mex. Fis. 64(6)(2018), 590–597.
[2] Agüero, M.A., De Lourdes Najera, M.A. and Carrillo, M. Nonclassic solitonic structures in DNA’s vibrational dynamics, Int. J. Mod. Phys. B 22(16)(2008), 2571–2582.
[3] Ali, K.K., Cattani, C., Gómez-Aguilar, J.F., Baleanu, D. and Os-man, M.S. Analytical and numerical study of the DNA dynamics aris-ing in oscillator-chain of Peyrard-Bishop model, Chaos Solit. Fractals. 139(2020), 110089.
[4] Al-Smadi, M., Freihat, A., Khalil, H., Momani, S. and Ali Khan, R. Numerical multistep approach for solving fractional partial differential equations, Int. J. Comput. Methods, 14(03) (2017), 1750029.
[5] Alvarez, A., Romero, F.R., Archilla, J.F., Cuevas, J. and Larsen, P. Breather trapping and breather transmission in a DNA model with an interface, Eur. Phys. J. B 51(2006), 119–130.
[6] Bayrak, M.A. and Demir, A. A new approach for space-time fractional partial differential equations by residual power series method, Appl. Math. Comput. 336(2018), 215–230.
[7] Behbahan, A. S., Alizadeh, A. A., Mahmoudi, M., Shamsborhan, M., Al-Musawi, T. J.and Pasha, P. A new Adomian decomposition technique for a thermal analysis forced non-Newtonian magnetic Reiner-Rivlin vis-coelastic fluid flow, Alex. Eng. J. 80(2023), 48–57.
[8] Benhammouda, B. The differential transform method as an effective tool to solve implicit Hessenberg index-3 differential‐algebraic equations, J. Math. 2023(1)(2023), 3620870.
[9] Chabchoub, A., Hoffmann, N.P. and Akhmediev, N. Rogue wave obser-vation in a water wave tank, Phys. Rev. Lett. 106(20)(2011), 204502.
[10] Chakrabarty, A.K., Roshid, M.M., Rahaman, M.M., Abdeljawad, T. and Osman, M.S., Dynamical analysis of optical soliton solutions for CGL equation with Kerr law nonlinearity in classical, truncated M-fractional derivative, beta fractional derivative, and conformable fractional deriva-tive types, Results Phys. 60, (2024) 107636.
[11] Chen, F.F. Introduction to plasma physics and controlled fusion, New York, Plenum press,1 (1984), 19–51.
[12] Chen, Y.Q., Tang, Y.H., Manafian, J., Rezazadeh, H. and Osman, M.S., Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model, Nonlinear Dyn.105 (2021) 2539–2548.
[13] Dauxois, T. Dynamics of breather modes in a nonlinear “helicoidal” model of DNA, Phys. Lett. A, 159(8-9) (1991), 390–395.
[14] Dusuel, S., Michaux, P. and Remoissenet, M. From kinks to compacton-like kinks, Phys. Rev. E, 57(2)(1998), 2320.
[15] El-Ajou, A. Adapting the Laplace transform to create solitary solutions for the nonlinear time-fractional dispersive PDEs via a new approach, Eur. Phys. J. Plus 136(2)(2021), 229.
[16] El-Ajou, A. and Al-Zhour, Z. A vector series solution for a class of hyperbolic system of Caputo time-fractional partial differential equations with variable coefficients, Front. Phys, 9(2021), 525250.
[17] El-Ajou, A., Arqub, O.A. and Momani, S. Approximate analytical solu-tion of the nonlinear fractional KdV–Burgers equation: a new iterative algorithm, J. Comput.l Phys. 293(2015),81–95.
[18] Hossain, M.N., Miah, M.M., Ganie, A.H., Osman, M.S. and Ma, W.X., Discovering new abundant optical solutions for the resonant nonlinear Schrödinger equation using an analytical technique, Opt. Quantum Elec-tron. 56(5), |(2024) 847.
[19] Hosseini, K., Alizadeh, F., Hinçal, E., Kaymakamzade, B., Dehingia, K. and Osman, M.S., A generalized nonlinear Schrödinger equation with logarithmic nonlinearity and its Gaussian solitary wave, Opt. Quantum Electron. 56(6) (2024) 929.
[20] İnç, M., Korpinar, Z. S., Al Qurashi, M. M. and Baleanu, D. A new method for approximate solutions of some nonlinear equations: Residual power series method, Adv. Mech. Eng. 8(4)(2016), 1687814016644580.
[21] Iqbal, M.A., Ganie, A.H., Miah, M.M. and Osman, M.S., Extracting the ultimate new soliton solutions of some nonlinear time fractional PDEs via the conformable fractional derivative, Fractal Fract. 8(4) (2024) 210.
[22] Kumar, S., Dhiman, S.K., Baleanu, D., Osman, M.S. and Wazwaz, A.M., Lie symmetries, closed-form solutions, and various dynamical profiles of solitons for the variable coefficient (2+ 1)-dimensional KP equations, Symmetry, 14(3), (2022) 97.
[23] Linak, M.C., Tourdot, R. and Dorfman, K.D. Moving beyond Watson–Crick models of coarse grained DNA dynamics, J. Chem. Phys. 135(20)(2011) 5102.
[24] Liu, J., Nadeem, M., Osman, M.S. and Alsayaad, Y., 2024. Study of multi-dimensional problems arising in wave propagation using a hybrid scheme, Sci. Rep.14(1), (2024) 5839.
[25] Osman, M.S., Multi-soliton rational solutions for quantum Zakharov-Kuznetsov equation in quantum agnetoplasmas, Waves in Random and Complex Media, 26(4), (2016) 434–443.
[26] Peregrine, D.H. Water waves, nonlinear Schrödinger equations and their solutions,ANZIAM J. 25(1) (1983),16-43.
[27] Peyrard, M. and Bishop, A.R. Statistical mechanics of a nonlinear model for DNA denaturation, Phys. Rev. Lett. 62(23)(1989), 2755.
[28] Priyadarsini, D., Routaray, M. and Sahu, P.K., A new numerical ap-proach to the solution of the nonlinear Kawahara equation by using combined Taylor–Dickson approximation, Iranian Journal of Numerical Analysis and Optimization, 14(1), (2024) 20–43.
[29] Priyadarsini, D., Sahu, P.K. and Routaray, M., A Combined Taylor–Bernstein Approximation for Solving Non-linear Fitz-Hugh–Nagumo Equation, Inter. J. Appl. Comput. Math. 10(3), (2024) 110.
[30] Rahman, M.M., Murshed, M.M. and Akhter, N. Applications of the homotopy perturbation method for some linear and non-linear partial differential equations, Desimal: Jurnal Matematika, 6(2) (2023), 185–190.
[31] Sarker, S., Karim, R., Akbar, M.A., Osman, M.S. and Dey, P., Soliton solutions to a nonlinear wave equation via modern methods, J. Umm Al-Qura Univ.Appl. Sci. (2024)1–8.
[32] Yong, Z.,Li, P. On the time-fractional Navier–Stokes equations, Comput. Math. Appl, 73(2017), 874–891.
[33] Zdravković, S. and Satarić, M.V. Parameter selection in a Peyrard–Bishop–Dauxois model for DNA dynamics, Phys. Lett. A, 373(31)(2009), 2739–2745.
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