On Fractional Calculus and Certain Results Involving K2 - Function
fractional calculus, Riemann - Liouville fractional integrals and derivatives
Abstract
In the present paper a new function called K2 - function, which is an extension of the function defined by Miller and Ross[20], is introduced and studied by the author in terms of some special functions and derived the relations that exists between the K2- function and the operators of Riemann-Liouville fractional integrals and derivatives.
Downloads
How to Cite
References
M Dzrbashjan (1952) On the integral representation and uniqueness of some classes of entire functions(in Russian). 85(1), 29-32.
M Dzrbashjan (1960) On the integral transformations generated by the generalized Mittag -Leffler function(in Russian). 13(3), 21-63.
M Dzrbashjan (1966) Integral transforms and Representations of Functions in the complex Domain.
A Erdelyi, W Magnus, F Oberhettinger, F Tricomi (1955) Higher Transcendental Functions. 3.
R Gorenflo, A Kilbas, S Rogosin (1998) On the generalized mittag-leffler type functions. 7(3-4), 215-224.
R Grenflo, F Mainardi (1996) The Mittag-Leffler type function in the Riemann-Liouville fractional calculus. 215-225.
R Gorenflo, F Mainardi (1997) Fractional Calculus. 223-276.
P Humbert, R (1953) Sur la function de Mittag-Leffler et quelques unes de ses. Generalizations. 77, 180-185.
Virginia Kiryakova (2000) Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus. 118(1-2), 241-259.
G Mittag-Leffler (1903) Sur la nuovelle function Ea(x). 137(2), 554-558.
G Mittag-Leffler (1905) Sur la representation analytique de'une branche uniforme une function monogene. 29, 101-181.
S Samko, A Kilbas, O Marichev (1990) Fractional Integrals and Derivatives. Theory and Applications.
Adders Wiman (1905) Über die Nullstellen der Funktionen Ea(x). 29(0), 217-234.
E Rainville (1960) Special functions.
R (1953) A propos d'une Note M. Pierre Humbert. 236, 2031-2032.
A Kilbas, M Saigo (1995) Fractional integrals and derivatives of Mittag-Leffler type function(Russian English summary). 39(4), 22-26.
A Kilbas (2005) Journal of Fractional Calculus & Applications. 8, 113-126.
A Mathai, R Saxena (1978) The H-function with applications in Statistics and other disciplines.
M Sharma, R Jain (2009) A note on a generalized M-series as a special function of fractional Calculus. 12(4).
K Miller, B Ross (1993) Introduction to Fractional Calculus. 1-17.
Published
2011-07-11
Issue
Section
License
Copyright (c) 2011 Authors and Global Journals Private Limited

This work is licensed under a Creative Commons Attribution 4.0 International License.