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Optical and Quantum Electronics
Erschienen in: Optical and Quantum Electronics 2/2018

01.02.2018

Lie symmetry analysis and explicit solutions for the time fractional generalized Burgers–Huxley equation

verfasst von: Mustafa Inc, Abdullahi Yusuf, Aliyu Isa Aliyu, Dumitru Baleanu

Erschienen in: Optical and Quantum Electronics | Ausgabe 2/2018

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Abstract

In this work, we study the time fractional generalized Burgers–Huxley equation with Riemann–Liouville derivative via Lie symmetry analysis and power series expansion method. We transform the governing equation to nonlinear ordinary differential equation of fractional order using its Lie point symmetries. In the reduced equation, the derivative is in Erdelyi–Kober sense. We apply power series technique to derive explicit solutions for the reduced equation. The convergence of the obtained power series solutions are also derived. Some interesting Figures for the obtained solutions are presented.
Vorheriger Artikel Electromagnetically induced transparency in a quantum pseudo-dot with spin–orbit interaction
Nächster Artikel Scattering of Lommel beams by homogenous spherical particle in generalized Lorenz–Mie theory

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Literatur
Alquran, M., Al-Khaled, K., Sivasundaram, S., Jaradat, H.M.: Mathematical and numerical study of existence of bifurcations of the generalized fractional Burgers–Huxley equation. Nonlinear Stud. 24(1), 235–244 (2017)MathSciNetMATH
Az-Zobi, E.: On the reduced differential transform method and its application to the generalized Burgers–Huxley equation. Appl. Math. Sci. 8(177), 8823–8831 (2014)
Baleanu, D., Inc, M., Yusuf, A., Aliyu, A.I.: Lie symmetry analysis, exact solutions and conservation laws for the time fractional modified Zakharov–Kuznetsov equation. Nonlinear Anal. Model. Control 22(6), 861–876 (2017)MathSciNetCrossRef
Baleanu, D., Inc, M., Yusuf, A., Aliyu, A.I.: Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey–Dodd–Gibbon–Sawada–Kotera equation. Commun. Nonlinear Sci. Numer. Simul. 59, 222–234 (2018)MathSciNetCrossRef
Batiha, B., Noorani, M.S.M., Hashim, I.: Application of variational iteration method to the generalized Burgers–Huxley equation. Chaos Solitons Fract. 36(3), 660–663 (2008)CrossRefMATHADS
Biswas, A., Suarez, P.: Exact 1-soliton solution of the zakharov-kuznetsov equation in plasmas with power law nonlinearity. Appl. Math. Comput. 217(17), 7372–7375 (2011)MathSciNetCrossRefMATH
Biswas A, Morris R, Kara AH (2013) Soliton solution and conservation laws of the Zakharov-Kuznetsov equation in plasmas with power law nonlinearity
Biswas, A., Mirzazadeh, M., Eslami, M., Milovic, D.: Solitons in optical metamaterials by functional variable method and first integral approach. Frequenz 68(11–12), 525–530 (2014)ADS
Bluman, G.W., Kumei, S.: Symmetries and Differential Equations. Springer, New York (1989)CrossRefMATH
Cenesiz, Y., Baleanu, D., Kurt, A., Tasbozan, O.: New exact solutions of Burgers’ type equations with conformable derivative. Waves Random Complex Media 27, 103–116 (2017)MathSciNetCrossRefMATH
Diethelm, K.: The analysis of fractional differential equations. Springer, Berlin (2010)CrossRefMATH
Ekici, M., Mirzazadeh, M., Eslami, M., Zhou, Q., Moshokoa, S.P., Biswas, A., Belic, M.: Optical soliton perturbation with fractional-temporal evolution by first integral method with conformable fractional derivatives. Optik 127, 10659–10669 (2016)CrossRefADS
Ekici, M., Mirzazadeh, M., Eslami, M.: Optical solitons with Biswas–Milovic equation for power law and dual-power law nonlinearities. Nonlinear Dyn. 83(1–2), 731–738 (2017)MathSciNetMATH
Eslami, M.: Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations. Appl. Math. Comput. 285, 141–148 (2016)MathSciNet
Eslami, M., Mirzazadeh, M.: Trial solution technique to chiral nonlinear Schrodinger’s equation in (1 + 2)-dimensions. Nonlinear Dyn. 85(2), 813–816 (2016)MathSciNetCrossRef
Eslami, M., Rezazadeh, H.: The first integral method for Wu-Zhang system with conformable time-fractional derivative. Calcolo 53(3), 475–485 (2016)MathSciNetCrossRefMATH
Eslami, M., Zhou, Q., Moshokoa, S.P., Biswas, A., Belic, M., Ekici, M., Mirzazadeh, M.: Optical soliton pertubation with fractional temporal evolution by first integral method with conformabal fractional derivatives. Optik 127(22), 10659–10669 (2016)CrossRefADS
Eslami, M., Rezazadeh, H., Rezazadeh, M., Mosavei, S.S.: Exact solutions to the space-time fractional Schrödinger–Hirota equation and the space-time modified KDV-Zakharov–Kuznetsov equation. Opt. Quantum Electron. 49(8) (2017b). https://​doi.​org/​10.​1007/​s11082-017-1112-6
Galaktionov, V.A., Svirshchevskii, S.R.: Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics. Chapman and Hall/CRC, Boca Raton, Florida (2006)MATH
Gazizov, R.K., Kasatkin, A.A., Lukashcuk, S.Y.: Continuous transformation groups of fractional differential equations. Vestnik USATU 9, 125–135 (2007)
Gazizov, R.K., Kasatkin, A.A., Lukashcuk, S.Y.: Symmetry properties of fractional diffusion equations. Phys. Scr. 136, 014–016 (2009)
Guo, S., Mei, L.Q., Li, Y., Sun, Y.F.: The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics. Phys. Lett. A 376, 407–411 (2012)MathSciNetCrossRefMATHADS
Hashim, I., Noorani, M.S.M., Al-Hadidi, M.R.S.: Solving the generalized Burgers–Huxley equation using the Adomian decomposition method. Math. Comput. Model. 43, 1404–1411 (2006)MathSciNetCrossRefMATH
Hosseini, K., Ansari, R.: New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method. Waves Random Complex Media 27, 628–636 (2017)MathSciNetCrossRef
Hosseini, K., Manafian, J., Samadani, F., Foroutan, M., Mirzazadeh, M., Zhou, Q.: Resonant optical solitons with perturbation terms and fractional temporal evolution using improved tan (ϕ (η)/2)-expansion method and exp function approach. Optik 158, 933–939 (2018)CrossRefADS
Ibragimov, N.H.: Handbook of Lie Group Analysis of Differential Equations, vol. 1. CRC Press, Boca Raton (1994)MATH
Ibragimov, N.H.: Handbook of Lie Group Analysis of Differential Equations, vol. 2. CRC Press, Boca Raton (1995)MATH
Ibragimov, N.H.: Handbook of Lie Group Analysis of Differential Equations, vol. 3. CRC Press, Boca Raton (1996)
Inc, M., Yusuf, A., Aliyu, A.I., Baleanu, D.: Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: lie symmetry analysis, explicit solutions and convergence analysis. Phys. A 493, 94–106 (2018a)MathSciNetCrossRef
Jumarie, G.: Modified Riemann–Liouville derivative and fractional Taylor series of non differentiable functions further results. Comput. Math Appl. 51, 1367–1376 (2006)MathSciNetCrossRefMATH
Jumarie, G.: Cauchy’s integral formula via the modified Riemann–Liouville derivative for analytic functions of fractional order. Appl. Math. Lett. 23, 1444–1450 (2010)MathSciNetCrossRefMATH
Kiryakova, V.: Generalised Fractional Calculus and Applications. Pitman Research Notes in Mathematics, vol. 301. Longman, London (1994)
Kiryakova, V.: Generalised Fractional Calculus and Applications. Pitman Research Notes in Mathematics, vol. 301. Longman, London (1996)
Lie, S.: On integration of a class of linear partial differential equations by means of definite integrals. Arch. Math. Log. 6(3), 328–368 (1881)MATH
Liu, H.Z.: Complete group classifications and symmetry reductions of the fractional fifth-order KdV types of equations. Stud. Appl. Math. 131, 317–330 (2013)MathSciNetCrossRefMATH
Lu, B.: Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations. Phys. Lett. A 376, 2045–2048 (2012)MathSciNetCrossRefMATHADS
Mirzazadeh, M., Eslami, M., Vajargah, B.F., Biswas, A.: Application of the first integral method to fractional partial differential equations. Indian J. Phys. 88(2), 177–184 (2014)CrossRefADS
Mirzazadeh, M., Eslami, M., Biswas, A.: Solitons and other solutions to Boussinesq equation with power law nonlinearity and dual dispersion. Nonlinear Dyn. 84(2), 669–676 (2016)MathSciNetCrossRefMATH
Mirzazadeh, M., Eslami, M., Zerrad, E.: Optical solitons in nonlinear directional couplers by sine-cosine function method and Bernoulli’s equation approach. Nonlinear Dyn. 81(4), 1933–1949 (2017)MathSciNetCrossRefMATH
Neirameh, A., Eslami, M.: An analytical method for finding exact solitary wave solutions of the coupled (2 + 1)-dimensional Painlevé Burgers equation, Scientia Iranica. Trans. B Mech. Eng. 24(2), 715–726 (2017)
Olver, P.J.: Application of Lie Group to Differential Equation. Springer, New York (1986)CrossRef
Ovsiannikov, L.V.: Group Analysis of Differential Equations. Academic Press, New York (1982)MATH
Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)MATH
Qin, C.Y., Tian, S.F., Wang, X.B., Zhang, T.T.: Lie symmetries, conservation laws and explicit solutions for time fractional Rosenau–Haynam equation. Commun. Theor. Phys. 67, 157–165 (2017)CrossRefMATHADS
Rudin, W.: Principles of Mathematic Analysis. China Machine Press, Beijing (2004)
Sahadevan, R., Bakkyaraj, T.: Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations. J. Math. Anal. Appl. 393, 341–347 (2012)MathSciNetCrossRefMATH
Sonomezoglu, A., Eslami, M., Zhou, Q., Zerrad, E., Biswas, A., Belic, M., Ekici, M., Mirzazadeh, M.: Optical solitons in nano-fibers with fractional temporal evolution. J. Comput. Theor. Nanosci. 13(8), 5361–5374 (2016a)CrossRef
Sonomezoglu, A., Ortakaya, S., Eslami, M., Biswas, A., Mirzazadeh, M., Ekici, M.: Solitons solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics. Eur. Phys. J. Plus 131(6), 166–177 (2016b)
Tchier, F., Yusuf, A., Aliyu, A.I., Inc, M.: Soliton solutions and conservation laws for lossy nonlinear transmission line equation. Superlattices Microstruct. 107, 320–336 (2017)CrossRefADS
Vajargah, B.F., Mirzazadeh, M., Eslami, M., Biswas, A.: Solitons and periodic solutions to a couple of fractional nonlinear evolution equations. Pramana 82(3), 465–476 (2014)CrossRefADS
Wang, G.W., Liu, X.Q., Zhang, Y.Y.: Lie symmetry analysis to the time fractional generalized fifth-order KdV equation. Commun. Nonlinear Sci. Numer. Simul. 18, 2321–2326 (2013a)MathSciNetCrossRefMATHADS
Wang, G., Liu, X., Zhang, Y.: Lie symmetry analysis to the time fractional generalized fifth-order KdV equation. Commun Nonlinear Sci Numer Simulat 18, 2321–2326 (2013b)MathSciNetCrossRefMATHADS
Wang, G., Kara, A.H., Fakhar, K.: Symmetry analysis and conservation laws for the class of time-fractional nonlinear dispersive equation. Nonlinear Dyn. 82, 281–287 (2015)MathSciNetCrossRefMATH
Wazwaz, A.M.: Analytic study on Burgers, Fisher, Huxley equations and combined forms of these equations. Appl. Math. Comput. 195(2), 754–761 (2008)MathSciNetCrossRefMATH
Zerrad, E., Biswas, A., Kohl, R., Milovic, D.: Optical solitons by he’s variational principle in a non-kerr law media. J. Infrared Millim. Terahertz Waves 30(5), 526–537 (2009)CrossRef
Zerrad, E., Biswas, A., Song, M., Ahmed, B.: Domain wall and bifurcation analysis of the Klein-Gordon Zakharov–Kuznetsov equation in (1 + 2)-dimensions with power law nonlinearity. Chaos 23(3) (2013). https://​doi.​org/​10.​1063/​1.​4816346
Zhang, S., Zhang, H.Q.: Fractional sub-equation method and its applications to nonlinear fractional PDEs. Phys. Lett. A 375, 1069–1073 (2011)MathSciNetCrossRefMATHADS
Zhou, Q., Moshokoa, S.P., Biswas, A., Belic, M., Ekici, M., Mirzazadeh, M.: Solitons in optical metamaterials with fractional temporal evolution. Optik 127(22), 10879–10897 (2016)CrossRef
Metadaten
Titel
Lie symmetry analysis and explicit solutions for the time fractional generalized Burgers–Huxley equation
verfasst von
Mustafa Inc
Abdullahi Yusuf
Aliyu Isa Aliyu
Dumitru Baleanu
Publikationsdatum
01.02.2018
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 2/2018
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-018-1373-8

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