Skip to main content
Top
Published in:
Cover of the book

2024 | OriginalPaper | Chapter

High-Precision Method for Space-Time-Fractional Klein-Gordon Equation

Authors : A. Habjia, A. El Hajaji, J. El Ghordaf, K. Hilal, A. Charhabil

Published in: Applied Mathematics and Modelling in Finance, Marketing and Economics

Publisher: Springer Nature Switzerland

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper presents the space-time fractional Klein-Gordon equations (FKGEs) for the spinless particle in potential field. It defines to describe the Higgs boson and the propagation of a boson in vacuum in Standard Model (SM). Besides, in this paper, the sine method is employed to construct exact solutions of the space-time fractional Klein-Gordon equations. Many new families of exact traveling wave solutions of the space-time fractional Klein-Gordon equations are successfully obtained. It is shown that the proposed method provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

Dont have a licence yet? Then find out more about our products and how to get one now:

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 "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"

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!

Literature
1.
go back to reference Khan, T.U., Khan, M.A.: Generalized conformable fractional operators. J. Comput. Appl. Math.346, 378–389 (2019) Khan, T.U., Khan, M.A.: Generalized conformable fractional operators. J. Comput. Appl. Math.346, 378–389 (2019)
3.
go back to reference Wazwaz, A.M.: Compactons, solitons and periodic solutions for some forms of nonlinear Klein-Gordon equations. Chaos Solitons Fract. 4, 1005–1013 (2006) Wazwaz, A.M.: Compactons, solitons and periodic solutions for some forms of nonlinear Klein-Gordon equations. Chaos Solitons Fract. 4, 1005–1013 (2006)
4.
go back to reference Shallal, M.A., Jabbar, H.N., Ali, K.K.: Analytic solution for the space-time fractional Kein-Gordon and coupled conformable Boussinesq equations. Results Phys. 8, 372–378 (2018) Shallal, M.A., Jabbar, H.N., Ali, K.K.: Analytic solution for the space-time fractional Kein-Gordon and coupled conformable Boussinesq equations. Results Phys. 8, 372–378 (2018)
5.
go back to reference 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. Physica A 493, 94–106 (2018) 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. Physica A 493, 94–106 (2018)
6.
go back to reference Hashemizadeh, E., Ebrahimzadeh, A.: An efficient numerical scheme to solve fractional diffusion-wave and fractional Klein-Gordon equations in fluid mechanics. Physica A 503, 1189–1203 (2018) Hashemizadeh, E., Ebrahimzadeh, A.: An efficient numerical scheme to solve fractional diffusion-wave and fractional Klein-Gordon equations in fluid mechanics. Physica A 503, 1189–1203 (2018)
7.
go back to reference Tamsir, M., Srivastava, V.K.: Analytical study of time-fractional order Klein Gordon equation. Alexandria Eng. J. 55, 561–567 (2016) Tamsir, M., Srivastava, V.K.: Analytical study of time-fractional order Klein Gordon equation. Alexandria Eng. J. 55, 561–567 (2016)
8.
go back to reference 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) 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)
9.
10.
go back to reference Khalil, R., Horani, M.A., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014) Khalil, R., Horani, M.A., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)
11.
go back to reference Roy, R., Ali Akbar, M., Wazwaz, A.M.: Exact wave solutions for the nonlinear time fractional Sharma-Tasso-Olver equation and the fractional Klein-Gordon equation in mathematical physics. Opt. Quant. Electron. 50, 25 (2018) Roy, R., Ali Akbar, M., Wazwaz, A.M.: Exact wave solutions for the nonlinear time fractional Sharma-Tasso-Olver equation and the fractional Klein-Gordon equation in mathematical physics. Opt. Quant. Electron. 50, 25 (2018)
12.
go back to reference Aruna, K., Ravi Kanth, A.S.V.: Two-Dimensional differential transform method and modified differential transform method for solving nonlinear fractional Klein-Gordon equation. Natl. Acad. Sci. Lett. 37(2), 163–171 (2014) Aruna, K., Ravi Kanth, A.S.V.: Two-Dimensional differential transform method and modified differential transform method for solving nonlinear fractional Klein-Gordon equation. Natl. Acad. Sci. Lett. 37(2), 163–171 (2014)
13.
go back to reference Unsala, O., Gunerb, O., Bekira, A.: Analytical approach for space-time fractional Klein-Gordon equation. Optik 135, 337–345 (2017)CrossRef Unsala, O., Gunerb, O., Bekira, A.: Analytical approach for space-time fractional Klein-Gordon equation. Optik 135, 337–345 (2017)CrossRef
15.
go back to reference Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015) Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)
16.
go back to reference Liu, C.-S.: Counterexamples on Jumarie’s two basic fractional calculus formulae. Commun. Nonlinear Sci. Numer. Simul. 22(1), 924 (2015) Liu, C.-S.: Counterexamples on Jumarie’s two basic fractional calculus formulae. Commun. Nonlinear Sci. Numer. Simul. 22(1), 924 (2015)
17.
go back to reference Jumarie, G.: Modified Riemann-Liouville derivative and fractional taylor series of nondifferentiable functions further results. Comput. Math. Appl. 51, 9–10:1367–76 (2006) Jumarie, G.: Modified Riemann-Liouville derivative and fractional taylor series of nondifferentiable functions further results. Comput. Math. Appl. 51, 9–10:1367–76 (2006)
18.
go back to reference Bezák, V.: Variations on the linear harmonic oscillator: fourier analysis of a fractional schrodinger equation. Rep. Math. Phys. 84, No. 3 (2019) Bezák, V.: Variations on the linear harmonic oscillator: fourier analysis of a fractional schrodinger equation. Rep. Math. Phys. 84, No. 3 (2019)
19.
go back to reference Feng, W.: On symmetry groups and conservation laws for space-time fractional inhomogeneous nonlinear diffusion equation. Rep. Math. Phys. 84(3) (2019) Feng, W.: On symmetry groups and conservation laws for space-time fractional inhomogeneous nonlinear diffusion equation. Rep. Math. Phys. 84(3) (2019)
20.
go back to reference Wei, F., Zhao, S.-L.: Cauchy matrix type solutions for the nonlocal nonlinear Schrödinger equation. Rep. Math. Phys. 84(1) (2019) Wei, F., Zhao, S.-L.: Cauchy matrix type solutions for the nonlocal nonlinear Schrödinger equation. Rep. Math. Phys. 84(1) (2019)
21.
go back to reference Kudryashov, N.A.: Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons Fract. 24, 1217–1231 (2005) Kudryashov, N.A.: Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons Fract. 24, 1217–1231 (2005)
Metadata
Title
High-Precision Method for Space-Time-Fractional Klein-Gordon Equation
Authors
A. Habjia
A. El Hajaji
J. El Ghordaf
K. Hilal
A. Charhabil
Copyright Year
2024
DOI
https://doi.org/10.1007/978-3-031-42847-0_1

Premium Partners