nach oben

Optical and Quantum Electronics

Erschienen in:

01.03.2018

Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method

verfasst von: Hadi Rezazadeh, Alper Korkmaz, Mostafa Eslami, Javad Vahidi, Rahim Asghari

Erschienen in: Optical and Quantum Electronics | Ausgabe 3/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The generalized projective Riccati equation method is proposed to establish exact solutions for generalized form of the reaction Duffing model in fractional sense namely, Khalil’s derivative. The compatible traveling wave transform converts the governing equation to a non linear ODE. The predicted solution is a series of two new variables that solve a particular ODE system. Coefficients of terms in the series are calculated by solving an algebraic system that comes into existence by substitution of the predicted solution into the ODE which is the result of the wave transformation of the governing equation. Returning original variables give exact solutions to the governing equation in various forms.

Vorheriger Artikel Solitons for perturbed Gerdjikov–Ivanov equation in optical fibers and PCF by extended Kudryashov’s method

Nächster Artikel Quantum quantifiers of Raman photon pairs with relativistic motion

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)MathSciNetCrossRefMATH

Aminikhah, H., Sheikhani, A.R., Rezazadeh, H.: Sub-equation method for the fractional regularized long-wave equations with conformable fractional derivatives. Sci. Iran. Trans. B Mech. Eng. 23(3), 1048–1054 (2016)

Bekir, A., Guner, O.: Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method. Chin. Phys. B 22, 110202 (2013)CrossRef

Chen, Y., Li, B.: General projective Riccati equation method and exact solutions for generalized KdV-type and KdV-Burgers-type equations with nonlinear terms of any order. Chaos, Solitons Fractals 19, 977–984 (2004)ADSMathSciNetCrossRefMATH

Conte, R., Musette, M.: Link between solitary waves and projective Riccati equations. J. Phys. A Math. 25, 5609–5623 (1992)ADSMathSciNetCrossRefMATH

Ege, S.M., Misirli, E.: Solutions of the space-time fractional foam-drainage equation and the fractional Klein–Gordon equation by use of modified Kudryashov method. Int. J. Res. Advent Technol. 2, 384–388 (2014)

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 Int. J. Light Electron Opt. 127(22), 10659–10669 (2016)CrossRef

Eslami, M.: Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations. Appl. Math. Comput. 285, 141–148 (2016)MathSciNet

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., Vajargah, B.F., Mirzazadeh, M., Biswas, A.: Application of first integral method to fractional partial differential equations. Indian J. Phys. 88, 177–184 (2014)ADSCrossRef

Eslami, M., Khodadad, F.S., Nazari, F., Rezazadeh, H.: The first integral method applied to the Bogoyavlenskii equations by means of conformable fractional derivative. Opt. Quantum Electron. 49, 391 (2017a)CrossRef

Eslami, M., Rezazadeh, H., Rezazadeh, M., Mosavi, S.S.: Exact solutions to the space-time fractional Schrodinger–Hirota equation and the space-time modified KDV-Zakharov–Kuznetsov equation. Opt. Quantum Electron. 49(8), 279 (2017b)CrossRef

Gomez, C.A., Salas, A.H.: New exact solutions for the combined sinh-cosh-Gordon equation. Lecturas Matematicas. 27, 87–93 (2006)MathSciNetMATH

Guner, O., Bekir, A., Korkmaz, A.: Tanh-type and sech-type solitons for some space-time fractional PDE models. Eur. Phys. J. Plus 132, 92 (2017)CrossRef

He, J.H.: Exp-function method for fractional differential equations. Int. J. Nonlinear Sci. Numer. Simul. 14, 363–366 (2013)MathSciNetCrossRef

Hosseini, K., Bekir, A., Ansari, R.: New exact solutions of the conformable time-fractional Cahn–Allen and Cahn–Hilliard equations using the modified Kudryashov method. Optik Int. J. Light Electron Opt. 132, 203–209 (2017)CrossRef

Huang, D.J., Zhang, H.Q.: The extended first kind elliptic sub-equation method and its application to the generalized reaction Duffing model. Phys. Lett. A 344, 229–237 (2005)ADSCrossRefMATH

Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative? J. Comput. Appl. Math. 264, 65–70 (2014)MathSciNetCrossRefMATH

Khan, K., Akbar, M.A.: Traveling wave solutions of nonlinear evolution equations via the enhanced (G′/G)-expansion method. J. Egypt. Math. Soc. 22, 220–226 (2014)MathSciNetCrossRefMATH

Khodadad, F.S., Nazari, F., Eslami, M., Rezazadeh, H.: Soliton solutions of the conformable fractional Zakharov–Kuznetsov equation with dual-power law nonlinearity. Opt. Quantum Electron. 49(11), 84 (2017)CrossRef

Kim, J.J., Hong, W.P.: New solitary-wave solutions for the generalized reaction duffing model and their dynamics. Z. Naturforsch. A 59, 721–728 (2004)ADSCrossRef

Korkmaz, A.: Exact solutions of space-time fractional EW and modified EW equations. Chaos, Solitons Fractals 96, 132–138 (2017a)ADSMathSciNetCrossRefMATH

Korkmaz, A.: Exact solutions to (3 + 1) conformable time fractional Jimbo–Miwa, Zakharov–Kuznetsov and modified Zakharov–Kuznetsov equations. Commun. Theor. Phys. 67, 479–482 (2017b)ADSMathSciNetCrossRefMATH

Li, B., Chen, Y.: Nonlinear partial differential equations solved by projective Riccati equations Ansatz. Z. Naturforsch. 58, 511–519 (2003)ADS

Liu, X.Q., Jiang, S.: The sec_q−tanh_q-method and its applications. Phys. Lett. A 298, 253–258 (2002)ADSMathSciNetCrossRef

Ren, Y., Zhang, H.: New generalized hyperbolic functions and auto-Bäcklund transformation to find new exact solutions of the (2 + 1)-dimensional NNV equation. Phys. Lett. A 357, 438–448 (2006)ADSMathSciNetCrossRefMATH

Rezazadeh, H., Manafian, J., Samsami Khodadad, F., Nazari, F.: Traveling wave solutions for density-dependent conformable fractional diffusion–reaction equation by the first integral method and the improved tan(1/2φ(ξ))-expansion method. Opt. Quantum Electron. 50, 21 (2018)CrossRef

Rui-Min, W., Jian-Ya, G., Chao-Qing, D., Jie-Fang, Z.: Construction of new variable separation excitations via extended projective Ricatti equation expansion method in (2 + 1)-dimensional dispersive long wave systems. Int. J. Theor. Phys. 46(1), 102–115 (2007)MathSciNetCrossRef

Tian, B., Gao, Y.T.: Observable solitonic features of the generalized reaction duffing model. Z. Naturforsch. A 57, 39–44 (2002)ADSCrossRef

Yan, Z.Y.: Generalized method and its application in the higher-order nonlinear Schrodinger equation in nonlinear optical fibres. Chaos, Solitons Fractals 16, 759–766 (2003)ADSMathSciNetCrossRefMATH

Yan, Z., Zhang, H.: Explicit and exact solutions for the generalized reaction duffing equation. Commun. Nonlinear Sci. Numer. Simul. 4, 224–227 (1999)ADSMathSciNetCrossRefMATH

Younis, M., Zafar, A.: Exact solution to nonlinear differential equations of fractional order via (G′/G)-expansion method. Appl. Math. 5, 1–6 (2014)CrossRef

Zayed, E.M.E., Alurrfi, K.A.E.: The generalized projective Riccati equations method for solving nonlinear evolution equations in mathematical physics. Abstr. Appl. Anal. 2014, 259190 (2014)MathSciNetCrossRef

Zheng, B., Wen, C.: Exact solutions for fractional partial differential equations by a new fractional sub-equation method. Adv. Differ. Equ. 2013, 199 (2013)MathSciNetCrossRefMATH

Titel: Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method
verfasst von: Hadi Rezazadeh
Alper Korkmaz
Mostafa Eslami
Javad Vahidi
Rahim Asghari
Publikationsdatum: 01.03.2018
Verlag: Springer US
Erschienen in: Optical and Quantum Electronics / Ausgabe 3/2018
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-018-1416-1

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 3/2018

Optical double color image encryption scheme in the Fresnel-based Hartley domain using Arnold transform and chaotic logistic adjusted sine phase masks

Short and symmetric pulse in double Q-switching Nd:GdVO4 1.34 μm laser with AO and Co2+:MgAl2O4 saturable absorber

Integrated structural color array enabled by ultrathin silver film via cavity-enhanced absorption

Smoothed finite element method for time dependent analysis of quantum resonance devices

Modified Kudryashov method and its application to the fractional version of the variety of Boussinesq-like equations in shallow water

Transmission and tunneling time characteristics in light propagation through anisotropic double semiconductor layered structure