Novel solitons through optical fibres for perturbed cubic-quintic-septic nonlinear Schr\"{o}dinger-type equation

[1] T. Abdeljawad, On conformable fractional calculus. J. Comput. Appl. Math. 279 (2015) 57-–66.[2] M.A. Abdou, On the fractional order space-time nonlinear equations arising in plasma physics, Indian J. Phys. 93(4) (2019) 537–541.

[3] M.A. Akbar, L. Akinyemi, S.W. Yao, A. Jhangeer, H. Rezazadeh, M.M. Khater, H. Ahmad and M. Inc, Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method, Res. Phys. 25 (2021) 104228.

[4] L. Akinyemi, q-Homotopy analysis method for solving the seventh-order time-fractional Lax’s Korteweg–de Vries and Sawada–Kotera equations, Comp. Appl. Math. 38(4) (2019) 1–22.

[5] L. Akinyemi, O.S. Iyiola and U. Akpan, Iterative methods for solving fourth- and sixth-order time-fractional Cahn-Hillard equation, Math. Meth. Appl. Sci. 43(7) (2020) 4050—4074.

[6] L. Akinyemi, M. Senol and O.S. Iyiola, Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method, Math. Comput. Simul. 182 (2021) 211–233.

[7] L. Akinyemi, M. Senol and S.N. Huseen, Modified homotopy methods for generalized fractional perturbed Zakharov Kuznetsov equation in dusty plasma, Adv. Differ. Equ. 2021(1) (2021) 1–27.

[8] L. Akinyemi and O.S. Iyiola, Exact and approximate solutions of time-fractional models arising from physics via Shehu transform, Math. Meth. Appl. Sci. 43(12) (2020) 7442–7464.

[9] L. Akinyemi and O.S. Iyiola, A reliable technique to study nonlinear time-fractional coupled Korteweg-de Vries equations, Adv. Differ. Equ. 2020 (2020) 1–27.

[10] E.A. Az-Zo’bi, A reliable analytic study for higher-dimensional telegraph equation, J. Math. Comput. Sci. 18 (2018) 423—429.

[11] E.A. Az-Zo’bi, A. Yıldırım and W.A. AlZoubi, The residual power series method for the one-dimensional unsteady flow of a van der Waals gas, Physica A 517 (2019) 188—196.

[12] E.A. Az-Zo’bi, Exact Analytic Solutions for Nonlinear Diffusion Equations via Generalized Residual Power Series Method, International J. Math. Comput. Sci. 14(1) (2019) 69–78.

[13] E.A. Az-Zo’bi, New kink solutions for the van der Waals p-system, Math. Meth. Appl. Sci. 42(18) (2019) 6216–6226.

[14] E.A. Az-Zo’bi, Peakon and solitary wave solutions for the modified Fornberg-Whitham equation using simplest equation method, International J. Math. Comput. Sci. 14(3) (2019) 635–645.

[15] E.A. Az-Zobi, Modified Laplace decomposition method, World Appl. Sci. J. 18(11) (2012) 1481–1486.

[16] E.A. Az-Zobi, An Approximate Analytic Solution for Isentropic Flow by An Inviscid Gas Equations, Arch. Mech. 66(3) (2014) 203–212.

[17] E.A. Az-Zobi, Construction of Solutions for Mixed Hyperbolic Elliptic Riemann Initial Value System of Conservation Laws, Appl. Math. Model. 37 (2013) 6018–6024.

[18] E.A. Az-Zobi, K. Al-Khaled and A. Darweesh, Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method, Math. 7 (2019) 550.

[19] E.A. Az-Zobi, K. Al Dawoud, M.F. Marashdeh, Numeric-analytic solutions of mixed-type systems of balance laws, Appl. Math. Comput. 265 (2015) 133—143.

[20] E.A. Az-Zobi, On the reduced differential transform method and its application to the generalized Burgers-Huxley equation, Appl. Math. Sci. 8 (177) (2014) 8823—8831.

[21] E.A. Az-Zobi, M.O. Al-Amr, A. Yıldırım and W.A. AlZoubi, Revised reduced differential transform method using Adomian’s polynomials with convergence analysis, Math. Engin. Sci. Aerospace 11(4) (2020) 827–840.

[22] E.A. Az-Zobi, L. Akinyemi and A.O. Alleddawi, Construction of optical solitons for the conformable generalized model in nonlinear media, Modern Physics Letters B 35(24) (2021) 2150409.

[23] E.A. Az-Zobi, W.A. Alzoubi, L. Akinyemi, M. S¸enol and B.S. Masaedeh, A variety of wave amplitudes for the conformable fractional (2 + 1)-dimensional Ito equation, Modern Phys. Lett. B 35(15) (2021) 2150254.

[24] E.A. Az-Zobi, W.A. AlZoubi, L. Akinyemi, M. S¸enol, I.W. Alsaraireh and M. Mamat, Abundant closed-form solitons for time-fractional integro–differential equation in fluid dynamics, Opt. Quant. Electron. 53 (2021) 132.

[25] A. Boukhouima, K. Hattaf, E.M. Lotfi, M. Mahrouf, D.F. Torres and N. Yousfi, Lyapunov functions for fractionalorder systems in biology: Methods and applications, Chaos, Solitons Fractals 140 (2020) 110224.

[26] A. Biswas, M. Ekici, A. Sonomezoglu and M. Belic, Highly dispersive optical solitons with cubic-quintic–septic law by exp-expansion, Optik 186 (2019) 321—325.

[27] A. Biswas, M. Ekici, A. Sonomezoglu and M. Belic, Highly dispersive optical solitons with cubic–quintic–septic law by extended Jacobi’s elliptic function expansion, Optik 183 (2019) 571—578.

[28] A. Biswas, M. Ekici, A. Sonomezoglu and M. Belic, Highly dispersive optical solitons with cubic-quintic–septic law by F-expansion, Optik 182 (2019) 897–906.

[29] A. Biswas, Optical soliton perturbation with Radhakrishnan–Kundu–Laksmanan equation by traveling wave hypothesis, Optik 171 (2018) 217–220.

[30] A. Biswas, M. Ekici, A. Sonmezoglu and M.R. Belic, Highly dispersive optical solitons with cubic–quintic–septic law by extended Jacobi’s elliptic function expansion, Optik 183 (2019) 571-–578.

[31] A. Biswas, M. Ekici, A. Sonmezoglu and M.R. Belic, Highly dispersive optical solitons with cubic–quintic–septic law by exp-expansion, Optik, 186 (2019) 321–325. https://doi.org/10.1016/j.rinp.2020.103021.

[32] A. Biswas, A.H. Kara, Q. Zhou, A.K. Alzahrani and M.livoj R. Belic, Conservation laws for highly dispersive optical Solitons in birefringent fibers, Regul. Chaot. Dyn. 25 (2020) 166-–177.

[33] M. Ekici and A. Sonmezoglu, Optical solitons with Biswas–Arshed equation by extended trial function method, Optik 177 (2019) 13–20.

[34] B. Ghanbari, M.S. Osman and D. Baleanu, Generalized exponential rational function method for extended Zakharov–Kuznetsov equation with conformable derivative, Modern Phys. Lett. A 34(20) (2019) 1950155.

[35] O. Gonz´alez-Gaxiola, A. Biswas, A.K. Alzahrani and M.R. Belic, Highly dispersive optical solitons with a polynomial law of refractive index by Laplace–Adomian decomposition, J. Comput. Electron. 20 (2021) 1216—1223.

[36] J.H. He and F.Y. Ji, Two-scale mathematics and fractional calculus for thermodynamics, Thermal Sci. 23(4) (2019) 2131–2133.

[37] S.J. Johnston, H. Jafari, S.P. Moshokoa, V.M. Ariyan and D. Baleanu, Laplace homotopy perturbation method for Burgers equation with space-and time-fractional order, Open Phys. 14(1) (2016) 247–252.

[38] R. Khalil, Al M. Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014) 65–70.

[39] R.W. Kohl, A. Biswas, M. Ekici, Q. Zhou, S. Khan, A.S. Alshomrani and M.R. Belic, Highly dispersive optical soliton perturbation with cubic–quintic–septic refractive index by semi-inverse variational principle, Optik 199 (2019) 163322.

[40] R.W. Kohl, A. Biswas, M. Ekici, Q. Zhou, S. Khan, A.S. Alshomrani and M.R. Belic, Highly dispersive optical soliton perturbation with cubic–quintic–septic refractive index by semi-inverse variational principle, Optik 199 (2019) 163322. https://doi.org/10.1016/j.ijleo.2019.163322

[41] R.W. Kohl, A. Biswas, M. Ekici, Q. Zhou, S. Khan, A.S. Alshomrani and M.R. Belic, Sequel to highly dispersive optical soliton perturbation with cubic-quintic-septic refractive index by semi-inverse variational principle, Optik 203 (2020) 163451. https://doi.org/10.1016/j.ijleo.2019.163451

[42] O. Kolebaje, E. Bonyah and L. Mustapha, The first integral method for two fractional non-linear biological models, Discrete Continuous Dynamical Syst. 12(3) (2019) 487.

[43] N.A. Kudryashov, First integrals and general solutions of the Biswas–Milovic equation, Optik 210 (2020) 164490.

[44] A. Kurt, A. Tozar and O.Tasbozan Applying the new extended direct algebraic method to solve the equation of obliquely interacting waves in shallow waters, J. Ocean Univ. China 19(4) (2020) 772–780.

[45] A. Kumar, R. Komaragiri and M. Kumar, Design of efficient fractional operator for ECG signal detection in implantable cardiac pacemaker systems, Int. J. Circuit Theory Appl. 47(9) (2019) 1459–1476.

[46] M.S. Osman, A. Korkmaz, H. Rezazadeh, M. Mirzazadeh, M. Eslami and Q. Zhou, The unified method for conformable time-fractional Schrodinger equation with perturbation terms, Chinese J. Phys. 56(5) (2018) 2500–2506.

[47] I. Owusu-Mensah, L. Akinyemi, B. Oduro and O.S. Iyiola, A fractional order approach to modeling and simulations of the novel COVID-19, Adv. Differ. Equ. 2020(1) (2020) 1–21.

[48] E. Pellegrino, L. Pezza and F. Pitolli, A collocation method in spline spaces for the solution of linear fractional dynamical systems, Math. Comput. Simulat. 176 (2020) 266–278.

[49] N.M. Rasheed, M.O. Al-Amr, E.A. Az-Zo’bi, M.A. Tashtoush and L. Akinyemi, Stable optical solitons for the higher-order Non-Kerr NLSE via the modified simple equation method, Math. 9 (2021) 1986.

[50] A.R. Seadawy, K.K. Ali and R.I. Nuruddeen, A variety of soliton solutions for the fractional Wazwaz-BenjaminBona Mahony equations, Results Phys. 12 (2019) 2234–2241.

[51] M. Senol, New analytical solutions of fractional symmetric regularized-long-wave equation, Revista Mexic. F´ıs. 66(3 May-Jun) (2020) 297–307.

[52] M. Senol, O.S. Iyiola, H. Daei Kasmaei and L. Akinyemi, Efficient analytical techniques for solving time-fractional nonlinear coupled Jaulent-Miodek system with energy-dependent Schr¨odinger potential. Adv. Differ. Equ. 2019 (2019) 1–21.

[53] M. Senol, Analytical and approximate solutions of (2 + 1)-dimensional time-fractional Burgers-KadomtsevPetviashvili equation, Commun. Theor. Phys. 72(5) (2020) 1–11.

[54] H.M. Srivastava, D. Baleanu, J.A.T. Machado, M.S. Osman, H. Rezazadeh, S. Arshed and H. Gunerhan, Traveling wave solutions to nonlinear directional couplers by modified Kudryashov method, Physica Scripta 95 (2020) 075217.

[55] O. Tasbozan, Y. C¸ enesiz, A. Kurt and D. Baleanu, New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method, Open Phys. 15(1) (2017) 647–651.

[56] N. Ullah, H.U. Rehman, M.A. Imran and T. Abdeljawad, Highly dispersive optical solitons with cubic law and cubic-quintic-septic law nonlinearities, Res. Phys. 17 (2020) 103021.

[57] G. Wang, Y. Liu, Y. Wu and X. Su, Symmetry analysis for a seventh-order generalized KdV equation and its fractional version in fluid mechanics, Fractals 28(3) (2020) 2050044–134.

[58] E.M.E. Zayed, M.E.M. Alngar, M.M. El-Horbaty, A. Biswas, M. Ekici, A.S. Alshomrani, S. Khan, Q. Zhou and M.R. Belic, Optical solitons in birefringent fibers having anti-cubic nonlinearity with a few prolific integration algorithms, Optik 200 (2020) 163229.

[59] E.M.E. Zayed, M.E.M. Alngar, M.M. El-Horbaty, A. Biswas, M. Ekici, Q. Zhou, S. Khan, F. Mallawi and M.R. Belic, Highly dispersive optical solitons in the nonlinear Schr¨odinger’s equation having polynomial law of the refractive index change, Indian J. Phys. 95 (2021) 109—119.