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Journal of Computational Electronics

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13-08-2021

Optical and W-shaped bright solitons of the conformable derivative nonlinear differential equation

Authors: Hamadou Halidou, Alphonse Houwe, Souleymanou Abbagari, Mustafa Inc, Serge Y. Doka, Thomas Bouetou Bouetou

Published in: Journal of Computational Electronics | Issue 5/2021

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Abstract

In this paper, we construct diverse solitary wave solutions for the nonlinear differential equation governing wave propagation in the low-pass nonlinear electrical transmission lines with conformable derivatives. However, by employing the new extended direct algebraic method and the improved Sub-ODE equation, we recovered W-shape bright soliton, dark soliton, periodic solutions, rational solutions and Weierstrass elliptic function solutions. The obtained results are new in nonlinear electrical transmission lines field. In addition, the acquired solitons are depicted with the appropriate parameters values of the methods and the nonlinear electrical transmission lines. The shape of the W-bright and dark soliton solutions points out the effect of the derivative order. Finally, the results indicate that the two integrations methods are a most applicable and forceful integration tools for emphasizing the soliton solutions.

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Aminikhah, H., Sheikhani, A.R., Rezazadeh, H.: Sub-equation method for the fractional regularized long-wave equations with conformable fractional derivatives. Sci. Iran. 3, 1048–1054 (2016)

Korkmaz, A., Hepson, O.E., Hosseini, K., Rezazadeh, H., Eslami, M.: Sine-Gordon expansion method for exact solutions to conformable time fractional equations in RLW-class. J. King Saud Univ.-Sci. 32, 567–574 (2020)CrossRef

Houwe, A., Sabi’u, J., Hammouch, Z., Doka, S.Y.: Solitary pulses of the conformable derivative nonlinear differential equation governing wave propagation in low-pass electrical transmission line. Phys. Scr. 95, 1–15 (2020)

Hammouch, Z., Mekkaoui, T.: Travelling-wave solutions for some fractional partial differential equation by means of generalized trigonometry functions. Int. J. Appl. Math. Res. 1, 206–212 (2012)CrossRef

Sabi’u, J., Jibril, A., Gadu, A.M.: New exact solution for the (3+1) conformable space-time fractional modified Korteweg-de-Vries equations via Sine–Cosine Method. J. Taibah Univ. Sci. 13, 91–95 (2019)

Owolabi, K.M., Hammouch, Z.: Mathematical modeling and analysis of two-variable system with noninteger-order derivative. Chaos 29, 013145–15 (2019)MathSciNetMATHCrossRef

Khan, H., Jarad, F., Abdeljawad, T., Khan, A.: A singular ABC-fractional differential equation with p-Laplacian operator. Chaos, Solitons Fractals 129, 56–61 (2019)MathSciNetMATHCrossRef

Singh, J., Kumar, D., Hammouch, Z., Atangana, A.: A fractional epidemiological model for computer viruses pertaining to a new fractional derivative. Appl. Math. Comput. 316, 504–515 (2018)MathSciNetMATH

Yang, X.J., Machado, J.A.T., Nieto, J.J.: A new family of the local fractional PDEs. Fundam. Inf. 151, 63–75 (2017)MathSciNetMATH

10.

Rezazadeh, H., Inc, M., Baleanu, D.: New solitary wave solutions for variants of \((3+1)\)-dimensional Wazwaz–Benjamin–Bona–Mahony equations. Front. Phys. 8, 1–11 (2020)CrossRef

11.

Vahidi, J., Masood Zekavatmand, S., Rezazadeh, H., Inc, M., Akinlar, M.A., Chu, Y.M.: New solitary wave solutions to the coupled Maccari’s system. Results Phys. 21, 1–11 (2021)

12.

Bansal, M.K., Kumar, D.: On the integral operators pertaining to a family of incomplete I-functions. AIMS Math. 5, 1247–1259 (2020)MathSciNetCrossRef

13.

Hashemi, M.S., Inc, M., Yusuf, A.: On three-dimensional variable order time fractional chaotic system with nonsingular kernel. Chaos Solitons Fractals. 133, 1–8 (2020)MathSciNetCrossRef

14.

Inc, M., Kilic, B.: Classification of travelling wave solutions for the time- fractional fifth-order KdV-like equation. Waves Random Complex Media 24, 393–403 (2014)MathSciNetMATHCrossRef

15.

Kilic, B., Inc, M.: The first integral method for the time fractional Kaup–Boussinesq system with time dependent coefficient. Appl. Math. Comput. 254, 70–74 (2015)MathSciNetMATH

16.

Prakash, A., Goyal, M., Baskonus, H.M., Gupta, S.: A reliable hybrid numerical method for a time dependent vibration model of arbitrary order. AIMS Math. 5, 979–1000 (2020)MathSciNetCrossRef

17.

Atangana, A.: Fractional discretization. The Africanish tortoise walk. Chaos Solitons Fractals 130, 109399 (2020)MathSciNetCrossRef

18.

Kumar, D., Singh, J., Baleanu, D.: Modified Kawahara equation within a fractional derivative with non-singular Kernel. Therm. sci. 22, 789–796 (2018)CrossRef

19.

Atangana, A., Alkahtani, B.S.T.: Analysis of the Kelleri–Segel model with a fractional derivative without singular kernel. Entropy 17, 4439–4453 (2015)MathSciNetMATHCrossRef

20.

Orkun, T., Senol, M., Kurt, A., Özkanc, O.: New solutions of fractional Drinfeld–Sokolov–Wilson system in shallow water waves. Ocean Eng. 161, 62–68 (2018)CrossRef

21.

Rezazadeh, H., Khodadad, F.S., Manafian, J.: New structure for exact solutions nonlinear time fractional Sharma–Tasso–Olver equation via conformable fraction derivative. Appl. Appl. Math. Int. J. 12, 405–414 (2017)MATH

22.

Rezazadeh, H., Korkmaz, A., Eslami, M., Vahidi, J., Asghari, R.: Traveling wave solution of conformable fractional generalized reaction Dufing model by generalized projective Riccati equation method. Opt. Quantum Electron. 50, 1–13 (2018)CrossRef

23.

Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives Theory and Applications. Gordon and Breach, New York (1993)MATH

24.

Igor, P.: Fractional Diferential Equations, 1st edn. Academic Press(1998)

25.

Abdon, A., Dumitru, B., Alsaedi, A.: New properties of conformable derivative. Open Math. 13, 8891–898 (2015)MathSciNetMATH

26.

Sousa, J.V.D.C., Oliviera, E.: A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties. Int. J. Anal. Appl. 16, 83–96 (2018)MATH

27.

Costa, A., Alfred Osborne, R., Donald, T., Resio, S., Alessio Chrivì, E., Saggese, E., Bellomo, K., Chuck Long, E.: Soliton turbulence in shallow water ocean surface waves. Phys. Rev. Lett. 113, 108501–5 (2014)CrossRef

28.

Ekici, M., Mirzazadeh, M., Sonmezoglu, A., Biswas, A.: Optical solitons with anti-cubic nonlinearity by extended trial equation method. Optik 136, 368–373 (2017)CrossRef

29.

Rezazadeh, H., Tariq, H., Eslami, M., Mirzazadeh, M., Zhou, Q.: New exact solutions of nonlinear conformable time-fractional Phi-4 equation. Chin. J. Phys. 56, 2805–2816 (2018)CrossRef

30.

Ali, A., Seadawy, A.R., Lu, D.: Soliton solutions of the nonlinear Schrödinger equation with the dual power law nonlinearity and resonant nonlinear Schrödinger equation and their modulation instability analysis. Optik 145, 79–88 (2017)CrossRef

31.

Zayed, E.M.E., Alurrfi, K.A.E.: New extended auxiliary equation method and its applications to nonlinear Schrödinger-type equations. Optik 127, 9131–9151 (2016)CrossRef

32.

Mirzazadeh, M., Alqahtani, R.T., Biswas, A.: Optical soliton perturbation with quadratic-cubic nonlinearity by Riccati–Bernoulli sub-ODE method and Kudryashov’s scheme. Optik 145, 74–78 (2017)

33.

Gabshi, M.A., Krishnan, E.V., Alquran, A., Al-Khaled, K.: Jacobi elliptic function solutions of a nonlinear Schrödinger equation in metamaterials. Nonlinear Stud. 3, 469–480 (2017)MATH

34.

Jawad, A.J.M., Mirzazadeh, M., Zhou, Q., Biswas, A.: Optical solitons with anti-cubic nonlinearity using three integration schemes. Superlattices Microstruct. 105, 1–10 (2017)CrossRef

35.

Seadawy, A.R.: Stability analysis of traveling wave solutions for generalized coupled nonlinear KdV equations. Appl. Math. Inf. Sci. 1, 209–14 (2016)CrossRef

36.

Qin, Z., Liu, L., Liu, Y., Yu, H., Yao, P., Wei, C., Zhang, H.: Exact optical solitons in metamaterials with cubic quintic nonlinearity and third-order dispersion. Nonlinear Dyn. 3, 1365–1371 (2015)

37.

Eslami, M., Rezazadeh, H.: The first integral method for Wu-Zhang system with conformable time-fractional derivative. Calcolo 3, 475–85 (2016)MathSciNetMATHCrossRef

38.

Tchier, F., Inc, M., Korpinar, Z., Baleanu, D.: Solution of the time fractional reaction-diffusion equations with residual power series method. Adv. Mech. Eng. 10, 11–10 (2016)

39.

Hammouch, Z., Mekkaoui, T., Agarwal, P.: Optical solitons for the Calogero–Bogoyavlenskii–Schiff equation in \((2+1)\) dimensions with time-fractional conformable derivative. Eur. Phys. J. Plus 248, 1–6 (2018)

40.

Houwe, A., Boudoue Hubert, M., Savaissoub, N., Jerome, D., Justin, M., Betchewe, G., Doka, Timoleon, S.Y., Crepin, K., Khang, S., Biswas, A., Ekici, M., Adesanya, S., Seithuti Moshokoah, S.P.S., Belic, M. : Optical solitons for higher-order nonlinear Schrödinger equation with three exotic integration architectures. Optik 179, 861–866 (2019)

41.

Hubert Malwe, B., Betchewe, G., Doka, S.Y., Crepin Kofane, T.: Travelling wave solutions and soliton solutions for the nonlinear transmission line using the generalized Riccati equation mapping method. Nonlinear Dyn. 84, 171–177 (2016)MathSciNetMATHCrossRef

42.

Rezazadeh, H., Mehdi Mirhosseini-Alizamini, S., Eslami, M., Abbagari, S.: New optical solitons of nonlinear conformable fractional Schrödinger–Hirota equation. Optik 172, 545–553 (2018)CrossRef

43.

Akinyemi, L., Rezazadeh, H., Yao, S.W., Ali Akbar, M., Mostafa Khater, M.A., Jhangeer, A., Inc, M., Ahmad, H.: Nonlinear dispersion in parabolic law medium and its optical solitons. Results Phys. 26, 1–9 (2021)CrossRef

44.

Ali Akbar, M., Akinyemi, L., Yao, S.W., Jhangeer, A., Rezazadeh, H., Mostafa Khater, M.A., Ahmad, H., Inc, M.: Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method. Results Phys. 25, 1–10 (2021)CrossRef

45.

Ahmad, H., Tufail Khan, A., Ahmad, I., Predrag Stanimirovi, S., Chu, Y.M.: A new analyzing technique for nonlinear time fractional Cauchy reaction–diffusion model equations. Results Phys. 19, 1–8 (2020)CrossRef

46.

Ahmad, H., Akgül, A., Tufail Khan, A., Predrag Stanimirovic, S., Chu, Y.M.: New perspective on the conventional solutions of the nonlinear time-fractional partial differential equations. Hindawi 2020, 1–10 (2020)MATH

47.

Ahmad, H., Tufail Khan, A.: Variational iteration algorithm-I with an auxiliary parameter for wave-like vibration equations. J. Low Freq. Noise, Vibr. Active Control 38, 1113–1124 (2019)CrossRef

48.

Ahmad, H., Tufail Khan, A., Predrag Stanimirovic, S., Chu, Y.M., Ahmad, I.: Modified variational iteration algorithm-II: convergence and applications to diffusion models. Hindawi 2020, 1–14 (2020)MATH

49.

Ahmad, I., Ahmad, H., Inc, M., Yao, S.W., Almohsen, B.: Application of local meshless method for the solution of two term time fractional-order multi-dimensional PDE arising in heat and mass transfer. Therm. Sci. 24, 95–105 (2020)CrossRef

50.

Inc, M., Nawaz Khan, M., Ahmad, I., Yao, S.W., Ahmad, H., Thounthong, P.: Analysing time-fractional exotic options via efficient local meshless method. Results Phys. 19, 1–6 (2020)CrossRef

51.

Zayed, E.M.E., Alngar, M.E.M., Al-Nowehy, A.G.: On solving the nonlinear Schrödinger equation with an anti-cubic nonlinearity in presence of Hamiltonian perturbation terms. Optik 178, 488–508 (2019)CrossRef

52.

Li, Z.: Periodic wave solutions of a generalized KdV–mKdV equation with higher-order nonlinear terms. Z. Naturforsch. 56a, 649–657 (2010)CrossRef

53.

Chen, H.T., Zhang, H.Q.: New double periodic and multiple soliton solutions of the generalized (2+1)-dimensional Boussinnesq equation. Chaos Soliton Fractals 20, 4765–769 (2004)

54.

Wazwaz, A.M.: New solitary wave solutions to the modified forms of Degasperis–Procesi and Camassa–Holm equations. Appl. Math. Comput. 186, 130–141 (2007)MathSciNetMATH

55.

Wazwaz, A.M.: The tanh–coth method for new compactons and solitons solutions for the \(K(n, n)\) and the \(K(n +1, n+1)\) equations. Appl. Math. Comput. 188, 1930–1940 (2007)MathSciNetMATH

56.

Ibrahim, R.W., Meshram, C., Hadid, S.B., Momani, S.: Analytic solutions of the generalized water wave dynamical equations based on time-space symmetric differential operator. J. Ocean Eng. Sci. 5, 186–195 (2020)CrossRef

57.

Lu, D., Seadawy, A.R., Ali, A.: Dispersive analytical wave solutions of three nonlinear dynamical water waves models via modified mathematical method. Results Phys. 13, 102–177 (2019)CrossRef

58.

Burioni, R., Cassi, D., Sodano, P., Trombettoni, A., Vezzani, A.: Topological filters and high-pass/low-pass devices for solitons in inhomogeneous networks. Phys. Rev. E 73, 066624 (2006)CrossRef

Title: Optical and W-shaped bright solitons of the conformable derivative nonlinear differential equation
Authors: Hamadou Halidou
Alphonse Houwe
Souleymanou Abbagari
Mustafa Inc
Serge Y. Doka
Thomas Bouetou Bouetou
Publication date: 13-08-2021
Publisher: Springer US
Published in: Journal of Computational Electronics / Issue 5/2021
Print ISSN: 1569-8025
Electronic ISSN: 1572-8137
DOI: https://doi.org/10.1007/s10825-021-01758-9

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