Skip to main content
Erschienen in: Optical and Quantum Electronics 8/2017

01.08.2017

A simple technique for constructing exact solutions to nonlinear differential equations with conformable fractional derivative

verfasst von: Melike Kaplan, Ahmet Bekir, Mehmet Naci Ozer

Erschienen in: Optical and Quantum Electronics | Ausgabe 8/2017

Einloggen

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

search-config
loading …

Abstract

The modified simple equation method is an interesting technique to find new and more general exact solutions to the fractional differential equations in nonlinear sciences. In this paper, the method is applied to construct exact solutions of (2+1)-dimensional conformable time-fractional Zoomeron equation and the conformable space-time fractional EW equation.

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!

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!

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!

Literatur
Zurück zum Zitat Bekir, A., Guner, O., Ayhan, B., Cevikel, A.C.: Exact solutions for fractional differential-difference equations by \((G^{\prime }/G)\)-expansion method with modified Riemann-Liouville derivative. Adv. Appl. Math. Mech. 8(02), 293–305 (2016)MathSciNetCrossRef Bekir, A., Guner, O., Ayhan, B., Cevikel, A.C.: Exact solutions for fractional differential-difference equations by \((G^{\prime }/G)\)-expansion method with modified Riemann-Liouville derivative. Adv. Appl. Math. Mech. 8(02), 293–305 (2016)MathSciNetCrossRef
Zurück zum Zitat 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)MathSciNetCrossRef 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)MathSciNetCrossRef
Zurück zum Zitat Demiray, S.T., Pandir, Y., Bulut, H.: The investigation of exact solutions of nonlinear time-fractional Klein-Gordon equation by using generalized Kudryashov method. AIP Conf. Proc. 1637, 283–289 (2014)ADSCrossRef Demiray, S.T., Pandir, Y., Bulut, H.: The investigation of exact solutions of nonlinear time-fractional Klein-Gordon equation by using generalized Kudryashov method. AIP Conf. Proc. 1637, 283–289 (2014)ADSCrossRef
Zurück zum Zitat Diethelm, K.: The Analysis of Fractional Differential Equations. Springer, Berlin (2010)CrossRefMATH Diethelm, K.: The Analysis of Fractional Differential Equations. Springer, Berlin (2010)CrossRefMATH
Zurück zum Zitat 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(22), 10659–10669 (2016)ADSCrossRef 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(22), 10659–10669 (2016)ADSCrossRef
Zurück zum Zitat Eslami, M., Rezazadeh, H.: The first integral method for Wu-Zhang system with conformable time-fractional derivative. Calcolo 53, 475–485 (2016)MathSciNetCrossRefMATH Eslami, M., Rezazadeh, H.: The first integral method for Wu-Zhang system with conformable time-fractional derivative. Calcolo 53, 475–485 (2016)MathSciNetCrossRefMATH
Zurück zum Zitat Guner, O., Bekir, A., Korkmaz, A.: Dark soliton solutions of space-time fractional Sharma-Tasso-Olver and Potential Kadomtsev-Petviashvili equations. Commun. Theor. Phys. 6(2), 182–188 (2017a)ADSCrossRefMATH Guner, O., Bekir, A., Korkmaz, A.: Dark soliton solutions of space-time fractional Sharma-Tasso-Olver and Potential Kadomtsev-Petviashvili equations. Commun. Theor. Phys. 6(2), 182–188 (2017a)ADSCrossRefMATH
Zurück zum Zitat Guner, O., Korkmaz, A., Bekir, A.: Tanh-type and sech-type solitons for some space-time fractional PDE models. Eur. Phys. J. Plus 132(2), 92 (2017b)CrossRef Guner, O., Korkmaz, A., Bekir, A.: Tanh-type and sech-type solitons for some space-time fractional PDE models. Eur. Phys. J. Plus 132(2), 92 (2017b)CrossRef
Zurück zum Zitat Gurefe, Y., Sonmezoglu, A., Misirli, E.: Application of trial equation method to the nonlinear partial differential equations arising in mathematical physics. Pramana J. Phys. 77(6), 1023–1029 (2011)ADSCrossRef Gurefe, Y., Sonmezoglu, A., Misirli, E.: Application of trial equation method to the nonlinear partial differential equations arising in mathematical physics. Pramana J. Phys. 77(6), 1023–1029 (2011)ADSCrossRef
Zurück zum Zitat Hosseini, K., Mayeli, P., Ansari, R.: Modified Kudryashov method for solving the conformable time-fractional Klein-Gordon equations with quadratic and cubic nonlinearities. Optik 130, 737–742 (2017)ADSCrossRef Hosseini, K., Mayeli, P., Ansari, R.: Modified Kudryashov method for solving the conformable time-fractional Klein-Gordon equations with quadratic and cubic nonlinearities. Optik 130, 737–742 (2017)ADSCrossRef
Zurück zum Zitat Kaplan, M., Bekir, A., Akbulut, A., Aksoy, E.: The modified simple equation method for nonlinear fractional differential equations. Rom. J. Phys. 60(9–10), 1374–1383 (2015) Kaplan, M., Bekir, A., Akbulut, A., Aksoy, E.: The modified simple equation method for nonlinear fractional differential equations. Rom. J. Phys. 60(9–10), 1374–1383 (2015)
Zurück zum Zitat Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)MathSciNetCrossRefMATH Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)MathSciNetCrossRefMATH
Zurück zum Zitat Korkmaz, A.: Exact solutions of space-time fractional EW and modified EW equations. Chaos Soliton Fractals 96, 132–138 (2017)ADSMathSciNetCrossRef Korkmaz, A.: Exact solutions of space-time fractional EW and modified EW equations. Chaos Soliton Fractals 96, 132–138 (2017)ADSMathSciNetCrossRef
Zurück zum Zitat Korkmaz, A.: Exact solutions to (3+1) conformable time fractional Jimbo-Miwa, Zakharov-Kuznetsov and Modified Zakharov-Kuznetsov equations. Commun. Theor. Phys. 67(05), 479–482 (2017)ADSCrossRefMATH Korkmaz, A.: Exact solutions to (3+1) conformable time fractional Jimbo-Miwa, Zakharov-Kuznetsov and Modified Zakharov-Kuznetsov equations. Commun. Theor. Phys. 67(05), 479–482 (2017)ADSCrossRefMATH
Zurück zum Zitat Oldham, K.B., Spanier, F.: The Fractional Calculus. Academic Press, New York (1974)MATH Oldham, K.B., Spanier, F.: The Fractional Calculus. Academic Press, New York (1974)MATH
Zurück zum Zitat Pandir, Y., Baskonus, H.M., Bulut, H.: On the solution of nonlinear time-fractional generalized burgers equation by homotopy analysis method and modified trial equation method. Int. J. Model. Optim. 4(4), 305–309 (2014)CrossRef Pandir, Y., Baskonus, H.M., Bulut, H.: On the solution of nonlinear time-fractional generalized burgers equation by homotopy analysis method and modified trial equation method. Int. J. Model. Optim. 4(4), 305–309 (2014)CrossRef
Zurück zum Zitat Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)MATH Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)MATH
Zurück zum Zitat Sahoo, S., Saha Ray, S.: Improved fractional sub-equation method for (3+1)-dimensional generalized fractional KdV-Zakharov-Kuznetsov equations. Comput. Math. Appl. 70, 158–166 (2015)MathSciNetCrossRef Sahoo, S., Saha Ray, S.: Improved fractional sub-equation method for (3+1)-dimensional generalized fractional KdV-Zakharov-Kuznetsov equations. Comput. Math. Appl. 70, 158–166 (2015)MathSciNetCrossRef
Zurück zum Zitat Unal, E., Gokdogan, A.: Solution of conformable fractional ordinary differential equations via differential transform method. Optik 128, 264–273 (2017)ADSCrossRef Unal, E., Gokdogan, A.: Solution of conformable fractional ordinary differential equations via differential transform method. Optik 128, 264–273 (2017)ADSCrossRef
Zurück zum Zitat Zhou, Y., Cai, S., Liu, Q.: Bounded traveling waves of the (2+1)-dimensional Zoomeron equation. Math. Probl. Eng. 2015, 163597 (2015)MathSciNet Zhou, Y., Cai, S., Liu, Q.: Bounded traveling waves of the (2+1)-dimensional Zoomeron equation. Math. Probl. Eng. 2015, 163597 (2015)MathSciNet
Metadaten
Titel
A simple technique for constructing exact solutions to nonlinear differential equations with conformable fractional derivative
verfasst von
Melike Kaplan
Ahmet Bekir
Mehmet Naci Ozer
Publikationsdatum
01.08.2017
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 8/2017
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-017-1105-5

Weitere Artikel der Ausgabe 8/2017

Optical and Quantum Electronics 8/2017 Zur Ausgabe