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On Generalized Mittag-Leffler Function and Fractional Operators
IJCA Proceedings on National Conference on Advances in Technology and Applied Sciences
© 2014 by IJCA Journal
NCATAS - Number 1
Year of Publication: 2014
Amit Chouhan and Satish Saraswat. Article: On Generalized Mittag-Leffler Function and Fractional Operators. IJCA Proceedings on National Conference on Advances in Technology and Applied Sciences NCATAS(1):9-12, September 2014. Full text available. BibTeX
@article{key:article,
author = {Amit Chouhan and Satish Saraswat},
title = {Article: On Generalized Mittag-Leffler Function and Fractional Operators},
journal = {IJCA Proceedings on National Conference on Advances in Technology and Applied Sciences},
year = {2014},
volume = {NCATAS},
number = {1},
pages = {9-12},
month = {September},
note = {Full text available}
}
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
- Forman, G. 2003. An extensive empirical study of feature selection metrics for text classification. J. Mach. Learn. Res. 3 (Mar. 2003), 1289-1305.
- Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi. 1955. Higher Transcendental Functions. Vol. III. McGraw-Hill, New York.
- R. Hilfer (Ed. ). 2000. Application of Fractional Calculus in Physics. WorldScientific Publishing Company, Singapore, New Jersey, London and Hong Kong.
- K. S. Miller, and B. Ross. 1993. An introduction to fractional calculus and fractional differential equations. Wiley- New York.
- G. M. Mittag-Leffler. 1903. Sur la nouvelle fonction E?(x). C. R. Acad. Sci. Paris 137, 554-558.
- F. Oberhettinger. 1974. Tables of Mellins Transforms. Springer-Verlag. New York.
- T. R. Prabhakar. 1971. A singular integral equation with a generalized Mittag-Leffler function in the Kernel. Yokohama Math. J. 19, 7-15.
- E. D. Rainville. 1960. Special Functions. Macmillan- New York.
- R. K. Saxena, A. M. Mathai, and H. J. Haubold. 2002. On Fractional Kinetic Equations. Astrophysics and Space Sci. 282, 281-287.
- 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.
- 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.
- M. Saigo. 1978. A remark on integral operators involving the Guass hypergeometric function. Rep. College General Ed. , Kyushu Univ. 11, 135-143.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev. 1993. Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Yverdon (Switzerland).
- K. Shukla, and J. C. Prajapati. 2007. On a generalization of Mittag-Leffler function and its properties. J. Math. Anal. Appl. 336, 797-811.
- N. Sneddon. 1979. The Use of Integral Transforms. Tata McGraw-Hill, New Delhi.
- H. M. Srivastava, and H. L. Manocha. 1984. A Treatise on Generating Functions. John Wiley and Sons, New York.
- A. Wiman. 1905. Uber de fundamental satz in der theorie der funktionen E?(x). Acta Math. 29, 191-201