Generalized Miller-Ross Function and its Integral Representation

Mohd. Farman Ali; Renu Jain; Manoj Sharma3

doi:https://doi.org/10.14445/22315373/IJMTT-V16P504

International Journal of Mathematics Trends and Technology

Research Article | Open Access

Volume 16 | Number 1 | Year 2014 | Article Id. IJMTT-V16P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V16P504

Generalized Miller-Ross Function and its Integral Representation

Mohd. Farman Ali, Renu Jain, Manoj Sharma3

Abstract

In this paper we derive the results in the form of integral representation, associated with a new special function introduced by the author, which is generalization of Miller- Ross function and the extension of K2 function

Keywords

Fractional calculus operators, Generalized Miller-Ross function and Special functions.

References

[1] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North- Holland Mathematics Studies 204, Elsevier,Amsterdam(2006).
[2] A. Wiman, Ueber den Fundamentalsatz in der Theorie der Fuktionen, Acta Mathematica 29 191-201(1905).
[3] G. M. Mittag-Leffler, Sur la nuovelle function E α (x). C.R.Acad.Sci. Paris(2) 137, 554-558(1903).
[4] E.D.Rainville, Special Functions, Chelsia Publishing Company, New York(1968).
[5] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego(1999).
[6] Keith B. Oldham, Jerome Spanier, The Fractional Calculus; Theory and Applications of Differentiation and integration to Arbitrary Order, Academic Press, New York and London. ISBN 0-12-525550-0(1974).
[7] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, New York etc (1993).
[8] M. Sharma and R. Jain, A Note on a Generalized M-Series as a Special Function of Fractional Calculus, Fract. Calc. Appl. Ansal. 12(2009), No.4, 449-452.

Citation :

Mohd. Farman Ali, Renu Jain, Manoj Sharma3, "Generalized Miller-Ross Function and its Integral Representation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 16, no. 1, pp. 16-18, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V16P504