PL EN


Preferences help
enabled [disable] Abstract
Number of results
Journal
2013 | 11 | 10 | 1457-1462
Article title

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

Content
Title variants
Languages of publication
EN
Abstracts
EN
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.
Publisher

Journal
Year
Volume
11
Issue
10
Pages
1457-1462
Physical description
Dates
published
1 - 10 - 2013
online
19 - 12 - 2013
Contributors
  • Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran, alireza_1038@yahoo.com
  • Faculty of Mathematical Sciences, Islamic Azad University, Lahijan Branch, P.O. Box 1616, Lahijan, Iran, ah_refahi@yahoo.com
  • Faculty of Mathematical Sciences, Islamic Azad University, Lahijan Branch, P.O. Box 1616, Lahijan, Iran, krostami@guilan.ac.ir
References
  • [1] G. Dattoli, H.M. Srivastava, K. Zhukovsky, Appl. Math. Comput. 184, 979 (2007) http://dx.doi.org/10.1016/j.amc.2006.07.001[Crossref]
  • [2] G. Dattoli, P.E. Ricci, I. Khomasuridze, Int. Transf. Special Funct. 15, 309 (2004) http://dx.doi.org/10.1080/10652460410001673013[Crossref]
  • [3] G. Dattoli, P. E. Ricci, C. Cesarano, Appl. Anal.: Inter. J. 80, 379 (2001) http://dx.doi.org/10.1080/00036810108840999[Crossref]
  • [4] H.M. Srivastava, H.L. Manocha, A Treatise On Generating Functions (Wiley, NewYork, 1984)
  • [5] H.W. Gould, A.T. Hopper, Duke Math. J. 29, 51 (1962) http://dx.doi.org/10.1215/S0012-7094-62-02907-1[Crossref]
  • [6] G. Dattoli, A. Arena, Math. Comput. Model. 40, 877 (2004) http://dx.doi.org/10.1016/j.mcm.2004.10.017[Crossref]
  • [7] A. Aghili, A. Ansari, Anal. Appl. 9, 1 (2011) http://dx.doi.org/10.1142/S0219530511001765[Crossref]
  • [8] G. Dattoli, P.L. Ottaviani, A. Torte, L. Vazquez, Riv. Nuovo Cimento 20, 1 (1997)
  • [9] I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999)
  • [10] G.H. Hardy, Ramanujan: Twelve Lectures On Subjects Suggested By His Life And Work (Cambridge University Press, Cambridge, 1940)
  • [11] A.M. Wazwaz, Appl. Math. Comput. 169, 321 (2005) http://dx.doi.org/10.1016/j.amc.2004.09.054[Crossref]
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0195-3
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.