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Analytical solution for the conformable fractional telegraph equation by Fourier method

Year 2020, Volume: 2 Issue: 1, 1 - 6, 30.06.2020

Abstract

n this paper, the Fourier method is effectively implemented for solving a conformable fractional telegraph equation. We discuss and derive the analytical solution of the conformable fractional telegraph equation with nonhomogeneous Dirichlet boundary condition.

References

  • [1] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North Holland Mathematics Studies 204, Elsevier, New York, NY, USA, 2006.
  • [2] I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
  • [3] E. C. Eckstein, J. A.Goldstein, and M. Leggas. Themathematics of suspensions:Kac walks and asymptotic analyticity. Electronic Journal of Differential Equations, vol. 3, pp. 39-50, 1999.
  • [4] R. C. Cascaval, E. C. Eckstein, C. L. Frota, and J. A. Goldstein. Fractional telegraph equations, Journal of Mathematical Analysis and Applications, vol. 276, no. 1, pp. 145-159, 2002.
  • [5] J. Chen, F. Liu, and V. Anh, Analytical solution for the time fractional telegraph equation by the method of separating variables, Journal of Mathematical Analysis and Applications, vol. 338, no. 2, pp. 1364-1377, 2008.
  • [6] R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh. A new definition of fractional derivative, Journal of Computational and Applied Mathematics, vol. 264, pp. 65-70, 2014.
  • [7] T. Abdeljawad. On conformable fractional calculus, Journal of Computational and Applied Mathematics, vol. 279, pp. 57-66, 2015.
Year 2020, Volume: 2 Issue: 1, 1 - 6, 30.06.2020

Abstract

References

  • [1] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North Holland Mathematics Studies 204, Elsevier, New York, NY, USA, 2006.
  • [2] I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
  • [3] E. C. Eckstein, J. A.Goldstein, and M. Leggas. Themathematics of suspensions:Kac walks and asymptotic analyticity. Electronic Journal of Differential Equations, vol. 3, pp. 39-50, 1999.
  • [4] R. C. Cascaval, E. C. Eckstein, C. L. Frota, and J. A. Goldstein. Fractional telegraph equations, Journal of Mathematical Analysis and Applications, vol. 276, no. 1, pp. 145-159, 2002.
  • [5] J. Chen, F. Liu, and V. Anh, Analytical solution for the time fractional telegraph equation by the method of separating variables, Journal of Mathematical Analysis and Applications, vol. 338, no. 2, pp. 1364-1377, 2008.
  • [6] R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh. A new definition of fractional derivative, Journal of Computational and Applied Mathematics, vol. 264, pp. 65-70, 2014.
  • [7] T. Abdeljawad. On conformable fractional calculus, Journal of Computational and Applied Mathematics, vol. 279, pp. 57-66, 2015.
There are 7 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Saad Abdelkebir

Brahim Nouırı

Publication Date June 30, 2020
Acceptance Date April 3, 2020
Published in Issue Year 2020 Volume: 2 Issue: 1

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