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

• Autorzy: Alireza Ansari , Amirhossein Sheikhani , Sohrab Kordrostami
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

generating function   Mellin transform   fractional differential equation   partial fractional differential equation   Wright function  

• Czasopismo: Open Physics
• Rocznik: 2013
• Tom: 11
• Numer: 10
• Strony: 1457-1462

Daty

wydano

2013-10-01

online

2013-12-19

Twórcy

autor

Alireza Ansari

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

autor

Amirhossein Sheikhani

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

autor

Sohrab Kordrostami

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

Bibliografia

• [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]

Identyfikatory

DOI

10.2478/s11534-013-0195-3