GENERALIZED FRACTIONAL DERIVATIVE OPERATORS OF THE PRODUCT OF TWO MULTI-INDEX MITTAG-LEFFLER FUNCTIONS WITH APPLICATIONS
Keywords:
generalized fractional derivative operators, multi-index Mittag-Leffler function.DOI:
https://doi.org/10.17654/0972096023020Abstract
We establish the generalized fractional derivative operators of the product of two generalized multi-index Mittag-Leffler functions. Further, the Riemann-Liouville, Kober and Saigo fractional derivative operators of given functions are obtained.
Received: October 22, 2023
Accepted: December 11, 2023
References
A. Erdelye et al., Higher Transcendental Functions, Vol. I, McGraw-Hill, New York, London, 1953.
A. A. Kilbas and N. Sebastian, Generalized fractional integration of Bessel function of first kind, Integral Transform Spec. Funct. 19 (2008), 869-883.
A. K. Shukla and J. C. Prajapati, On a generalization of Mittag-Leffler function and its properties, J. Math. Anal. Appl. 336(2) (2007), 797-811.
E. M. Wright, The asymptotic expansion of the generalized hypergeometric function II, Proc. London Math. Soc. 46(2) (1940), 389-408.
F. Oberhettinger, Tables of Mellin Transforms, Springer, New York, 1974.
H. M. Srivastava, A contour integral involving Fox’s H-function, Indian J. Math. 14 (1972), 1-6.
J. Choi, D. Kumar and S. D. Purohit, Integral formulas involving a product of generalized Bessel functions of the first kind, Kyungpook Math. J. 56(1) (2016), 131-136.
J. Choi and P. Agarwal, A note on fractional integral operator associated with multiindex Mittag-Leffler functions, Filomat 30(7) (2016), 1931-1939.
J. L. Lavoie and G. Trottier, On the sum of certain Appell’s series, Ganita 20 (1969), 43-46.
K. K. Kataria and P. Vellaisamy, The k-Wright function and Marichev-Saigo-Maeda fractional operators, J. Anal. 23 (2015), 75-87.
M. Saigo, A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep. Kyushu Univ. 11 (1978), 135-143.
M. Saigo and N. Maeda, More generalization of fractional calculus, Transform Method & Special Functions, Bulgarian Academy of Sciences, Sofia, Vol. 96, 1998, pp. 386-400.
R. K. Saxena and R. K. Parmar, Fractional integration and differentiation of the generalized Mathieu series, Axioms 6 (2017), 18.
R. K. Saxena and K. Nishimoto, N-fractional calculus of generalized Mittag- Leffler functions, J. Fract. Calc. 37 (2010), 43-52.
R. K. Saxena and M. Saigo, Generalized fractional calculus of the H-function associated with the Appell function J. Fract. Calc. 19 (2001), 89-104.
T. Pohlen, The Hadamard product and universal power series, Ph.D. Thesis, Universität Trier, Trier, Germany, 2009.
T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J. 19 (1971), 7-15.
V. N. Mishra, D. L. Suthar and S. D. Purohit, Marichev-Saigo-Maeda fractional calculus operators, Srivastava polynomials and generalized Mittag-Leffler function, Cogent Mathematics 4 (2017), 1320830.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Licensing Terms:
This work is published by Pushpa Publishing House and is subject to the following conditions:
Attribution: You must credit Pushpa Publishing House as the original publisher. Include the publication title and author(s) if applicable.
No Derivatives: Modifying the work or creating derivative works is not permitted without prior written permission.
For more information or permissions beyond the scope of this license, contact Pushpa Publishing House.






Google h-index: