Advertisement

A New Integral Transform for Solving Higher Order Linear Ordinary Laguerre and Hermite Differential Equations

  • Seyed Ahmad Pourreza AhmadiEmail author
  • Hassan Hosseinzadeh
  • AllahBakhsh Yazdani Cherati
Original Paper
  • 21 Downloads

Abstract

In this work a new integral transform is introduced and applied to solve higher order linear ordinary Laguerre and Hermite differential equations. We compare present transform with other method such as Frobenius Method.

Keywords

Integral transform Laguerre differential equation Hermite differential equation Frobenius method 

Notes

References

  1. 1.
    Alimorad, H.D., Hesameddini, E., FakharZadeh, A.J.: Using Elzaki transform solving the Klein–Gordon equation. TWMS J. Pure Appl. Math. 7(2), 177–184 (2016)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Belgacem, F.B.M., Silambarasan, R.: Theory of natural transform. MESA 3(1), 105–135 (2012)zbMATHGoogle Scholar
  3. 3.
    Cho, I., Hwajoon, K.: The solution of Bessel’s equation by using integral Transform. Appl. Math. Sci. 7(122), 6069–6075 (2014)MathSciNetGoogle Scholar
  4. 4.
    Elzaki, T.M.: The new integral transform “Elzaki transform”. Global J. Pure Appl. Math. 7(1), 57–64 (2011)Google Scholar
  5. 5.
    Elzaki, T.M.: On the connections between Laplace and Elzaki transforms. Adv. Theor. Appl. Math. 6(1), 1–11 (2011)Google Scholar
  6. 6.
    Elzaki, T.M., Ezaki, S.M.: Solution of integro-differential equations by using ELzaki transform. Global J. Math. Sci. Theory Practical 3(1), 1–11 (2011)Google Scholar
  7. 7.
    Elzaki, T.M., Ezaki, S.M.: On the Elzaki transform and ordinary differential equation with variable coefficients. Adv. Theor. Appl. Math. 6(1), 13–18 (2011)Google Scholar
  8. 8.
    Hwajoon, K.: A note on the shifting theorems for the Elzaki transform. Int. J. Math. Anal. 8(10), 481–488 (2014) MathSciNetGoogle Scholar
  9. 9.
    Iyanaga, S., Kawada, Y. (eds.): Encyclopedic Dictionary of Mathematics, p. 1481. MIT Press, Cambridge (1980)Google Scholar
  10. 10.
    Kılıçman, A., Eltayeb, H.: A note on integral transforms and partial differential equations. Appl. Math. Sci. 4(3), 109–118 (2010)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Maleknejad, K., Hadizadeh, M.: A new computational method for Volterra-Fredholm integral equations. Comput. Math. Appl. 37(9), 1–8 (1999)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Rodrigues formula - Encyclopedia of Mathematics www.encyclopediaofmath.org. Retrieved 2018-04-18Google Scholar
  13. 13.
    Shah, K., Junaid, M., Ali, N.: Extraction of Laplace, Sumudu, Fourier and Mellin transform from the Natural transform. J. Appl. Environ. Biol. Sci. 5(9), 1–10 (2015)Google Scholar
  14. 14.
    Weisstein, Eric W.: Hermite Differential Equation. From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/Hermite differential equation.html
  15. 15.
    Zhang, J.: A Sumudu based algorithm for solving differential equations. Comput. Sci. J. Moldova 15(3), 45 (2007)MathSciNetGoogle Scholar
  16. 16.
    Zwillinger, D.: Handbook of Differential Equations, 3rd edn, p. 120. Academic Press, Boston, MA (1997)Google Scholar

Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MazandaranBabolsarIran

Personalised recommendations