CFP last date
20 January 2025
Call for Paper
February Edition
IJCA solicits high quality original research papers for the upcoming February edition of the journal. The last date of research paper submission is 20 January 2025

Submit your paper
Know more
The week's pick
Responsive image
SFLA-Based Line Balancing and Task Optimization in Master-Slave Controlled Hanger Transportation Systems for Garment Production

Duc Hoang Nguyen
Random Articles
Reseach Article

On Generalized Mittag-Leffler Function and Fractional Operators

Published on September 2014 by Amit Chouhan, Satish Saraswat
journal_cover_thumbnail

National Conference on Advances in Technology and Applied Sciences
Foundation of Computer Science USA
NCATAS - Number 1
September 2014
Authors: Amit Chouhan, Satish Saraswat
298fd231-8a03-4e25-a443-900d3fdf9e73

Amit Chouhan, Satish Saraswat . On Generalized Mittag-Leffler Function and Fractional Operators. National Conference on Advances in Technology and Applied Sciences. NCATAS, 1 (September 2014), 9-12.

@article{
author = { Amit Chouhan, Satish Saraswat },
title = { On Generalized Mittag-Leffler Function and Fractional Operators },
journal = { National Conference on Advances in Technology and Applied Sciences },
issue_date = { September 2014 },
volume = { NCATAS },
number = { 1 },
month = { September },
year = { 2014 },
issn = 0975-8887,
pages = { 9-12 },
numpages = 4,
url = { /proceedings/ncatas/number1/17941-1603/ },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Proceeding Article
%1 National Conference on Advances in Technology and Applied Sciences
%A Amit Chouhan
%A Satish Saraswat
%T On Generalized Mittag-Leffler Function and Fractional Operators
%J National Conference on Advances in Technology and Applied Sciences
%@ 0975-8887
%V NCATAS
%N 1
%P 9-12
%D 2014
%I International Journal of Computer Applications
Abstract

The paper is devoted to study properties of a generalized function of Mittag-Leffler type, including various fractional integral operators like Riemann – Liouville operator, Hilfer operator etc. Certain unified integral formulas including this function are established. Image of this function under Saigo operator is also obtained.

References
  1. Forman, G. 2003. An extensive empirical study of feature selection metrics for text classification. J. Mach. Learn. Res. 3 (Mar. 2003), 1289-1305.
  2. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi. 1955. Higher Transcendental Functions. Vol. III. McGraw-Hill, New York.
  3. R. Hilfer (Ed. ). 2000. Application of Fractional Calculus in Physics. WorldScientific Publishing Company, Singapore, New Jersey, London and Hong Kong.
  4. K. S. Miller, and B. Ross. 1993. An introduction to fractional calculus and fractional differential equations. Wiley- New York.
  5. G. M. Mittag-Leffler. 1903. Sur la nouvelle fonction E?(x). C. R. Acad. Sci. Paris 137, 554-558.
  6. F. Oberhettinger. 1974. Tables of Mellins Transforms. Springer-Verlag. New York.
  7. T. R. Prabhakar. 1971. A singular integral equation with a generalized Mittag-Leffler function in the Kernel. Yokohama Math. J. 19, 7-15.
  8. E. D. Rainville. 1960. Special Functions. Macmillan- New York.
  9. R. K. Saxena, A. M. Mathai, and H. J. Haubold. 2002. On Fractional Kinetic Equations. Astrophysics and Space Sci. 282, 281-287.
  10. R. K. Saxena, A. M. Mathai, and H. J. Haubold. 2010. Solutionsof certain fractional kinetic equations and a fractional diffusion equation. J. Math. Phys. 51, 103506.
  11. R. K. Saxena, and M. Saigo. 2005. Certain properties of fractional calculus operators associated with generalized Mittag-Leffler function. Fract. Calc. Appl. Anal. 8(2), 141-154.
  12. M. Saigo. 1978. A remark on integral operators involving the Guass hypergeometric function. Rep. College General Ed. , Kyushu Univ. 11, 135-143.
  13. S. G. Samko, A. A. Kilbas, and O. I. Marichev. 1993. Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Yverdon (Switzerland).
  14. K. Shukla, and J. C. Prajapati. 2007. On a generalization of Mittag-Leffler function and its properties. J. Math. Anal. Appl. 336, 797-811.
  15. N. Sneddon. 1979. The Use of Integral Transforms. Tata McGraw-Hill, New Delhi.
  16. H. M. Srivastava, and H. L. Manocha. 1984. A Treatise on Generating Functions. John Wiley and Sons, New York.
  17. A. Wiman. 1905. Uber de fundamental satz in der theorie der funktionen E?(x). Acta Math. 29, 191-201
Index Terms

Computer Science
Information Sciences

Keywords

Fractional Integral Operators Fractional Differential Operators Generalized Mittag-leffler Function Fox-wright (_p^)?_q -function