Skip to main content
SpringerLink
Log in

On the generating function e xt+yϕ(t) and its fractional calculus

  • Research Article
  • Published:
Central European Journal of Physics

Abstract

In this article, we derive the coefficient set {H m (x,y)} ∞ m=1 using the generating function ext+yϕ(t). When the complex function ϕ(t) is entire, using the inverse Mellin transform, and when ϕ(t) has singular points, using the inverse Laplace transform, the coefficient set is obtained. Also, bi-orthogonality of this set with its associated functions and its applications in the explicit solutions of partial fractional differential equations is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Dattoli, H.M. Srivastava, K. Zhukovsky, Appl. Math. Comput. 184, 979 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. G. Dattoli, P.E. Ricci, I. Khomasuridze, Int. Transf. Special Funct. 15, 309 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. G. Dattoli, P. E. Ricci, C. Cesarano, Appl. Anal.: Inter. J. 80, 379 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. H.M. Srivastava, H.L. Manocha, A Treatise On Generating Functions (Wiley, NewYork, 1984)

    MATH  Google Scholar 

  5. H.W. Gould, A.T. Hopper, Duke Math. J. 29, 51 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  6. G. Dattoli, A. Arena, Math. Comput. Model. 40, 877 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Aghili, A. Ansari, Anal. Appl. 9, 1 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  8. G. Dattoli, P.L. Ottaviani, A. Torte, L. Vazquez, Riv. Nuovo Cimento 20, 1 (1997)

    Google Scholar 

  9. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999)

    MATH  Google Scholar 

  10. G.H. Hardy, Ramanujan: Twelve Lectures On Subjects Suggested By His Life And Work (Cambridge University Press, Cambridge, 1940)

    Google Scholar 

  11. A.M. Wazwaz, Appl. Math. Comput. 169, 321 (2005)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran

    Alireza Ansari

  2. Faculty of Mathematical Sciences, Islamic Azad University, Lahijan Branch, P.O. Box 1616, Lahijan, Iran

    Amirhossein Refahi Sheikhani & Sohrab Kordrostami

Authors
  1. Alireza Ansari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amirhossein Refahi Sheikhani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sohrab Kordrostami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alireza Ansari.

About this article

Cite this article

Ansari, A., Sheikhani, A.R. & Kordrostami, S. On the generating function e xt+yϕ(t) and its fractional calculus. centr.eur.j.phys. 11, 1457–1462 (2013). https://doi.org/10.2478/s11534-013-0195-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11534-013-0195-3

Keywords

Search

Navigation