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

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Applied Mathematics and Modelling in Finance, Marketing and Economics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1114))

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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.

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References

  1. Khan, T.U., Khan, M.A.: Generalized conformable fractional operators. J. Comput. Appl. Math.346, 378–389 (2019)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Wazwaz, A.M.: Compactons, solitons and periodic solutions for some forms of nonlinear Klein-Gordon equations. Chaos Solitons Fract. 4, 1005–1013 (2006)

    Google Scholar 

  4. 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)

    Google Scholar 

  5. 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)

    Google Scholar 

  6. 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)

    Google Scholar 

  7. Tamsir, M., Srivastava, V.K.: Analytical study of time-fractional order Klein Gordon equation. Alexandria Eng. J. 55, 561–567 (2016)

    Google Scholar 

  8. 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)

    Google Scholar 

  9. Wazwaz, A.M.: A sine-cosine method for handling nonlinear wave equations. Math. Comput. Model 40, 499–508 (2004)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  11. 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)

    Google Scholar 

  12. 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)

    Google Scholar 

  13. Unsala, O., Gunerb, O., Bekira, A.: Analytical approach for space-time fractional Klein-Gordon equation. Optik 135, 337–345 (2017)

    Article  Google Scholar 

  14. Lyu, P., Vong, S.: A linearized and second-order unconditionally convergent scheme for coupled time fractional Klein-Gordon-Schrödinger equation. Wiley Periodicals Inc. (2018). https://doi.org/10.1002/num.22282

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

    Google Scholar 

  16. Liu, C.-S.: Counterexamples on Jumarie’s two basic fractional calculus formulae. Commun. Nonlinear Sci. Numer. Simul. 22(1), 924 (2015)

    Google Scholar 

  17. Jumarie, G.: Modified Riemann-Liouville derivative and fractional taylor series of nondifferentiable functions further results. Comput. Math. Appl. 51, 9–10:1367–76 (2006)

    Google Scholar 

  18. Bezák, V.: Variations on the linear harmonic oscillator: fourier analysis of a fractional schrodinger equation. Rep. Math. Phys. 84, No. 3 (2019)

    Google Scholar 

  19. Feng, W.: On symmetry groups and conservation laws for space-time fractional inhomogeneous nonlinear diffusion equation. Rep. Math. Phys. 84(3) (2019)

    Google Scholar 

  20. Wei, F., Zhao, S.-L.: Cauchy matrix type solutions for the nonlocal nonlinear Schrödinger equation. Rep. Math. Phys. 84(1) (2019)

    Google Scholar 

  21. Kudryashov, N.A.: Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons Fract. 24, 1217–1231 (2005)

    Google Scholar 

  22. Kudryashov, N.A.: Exact solitary waves of the Fisher equation. Phys. Lett. A 342, 99–106 (2005)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. LIRST Laboratory, FP, University of Sultan Moulay Slimane, Beni-Mellal, Morocco

    A. Habjia

  2. LERSEM Laboratory, ENCG, University of Chouaïb Doukkali, El Jadida, Morocco

    A. El Hajaji

  3. LAMSC Laboratoty, FST, University of Sultan Moulay Slimane, Beni-Mellal, Morocco

    J. El Ghordaf & K. Hilal

  4. Paris Sorbonne Nord University, Paris, France

    A. Charhabil

Authors
  1. A. Habjia
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  2. A. El Hajaji
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  3. J. El Ghordaf
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  4. K. Hilal
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  5. A. Charhabil
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Corresponding author

Correspondence to A. El Hajaji .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Sultan Moulay Slimane University, Beni-Mellal, Morocco

    Said Melliani

  2. Div of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, BC, CP, Baja California, Mexico

    Oscar Castillo

  3. National School of Trade and Management, Chouaib Doukkali University, El Jadida, Morocco

    Abdelmajid El Hajaji

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Habjia, A., Hajaji, A.E., Ghordaf, J.E., Hilal, K., Charhabil, A. (2024). High-Precision Method for Space-Time-Fractional Klein-Gordon Equation. In: Melliani, S., Castillo, O., El Hajaji, A. (eds) Applied Mathematics and Modelling in Finance, Marketing and Economics. Studies in Computational Intelligence, vol 1114. Springer, Cham. https://doi.org/10.1007/978-3-031-42847-0_1

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  • DOI: https://doi.org/10.1007/978-3-031-42847-0_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-42846-3

  • Online ISBN: 978-3-031-42847-0

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