publication . Article . 2016

On certain fractional calculus operators involving generalized Mittag-Leffler function

Dinesh Kumar;
Open Access English
  • Published: 01 Jun 2016 Journal: Sahand Communications in Mathematical Analysis (issn: 2322-5807, eissn: 2423-3900, Copyright policy)
  • Publisher: University of Maragheh
Abstract
The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators are the generalization of the Saigo fractional calculus operators. The established results provide extensions of the results given by Gupta and Parihar [3], Saxena and Saigo [30], Samko et al. [26]. On account of the general nature of the generalized Mittag-Leffler function...
Subjects
free text keywords: Marichev-Saigo-Maeda fractional calculus operators, Generalized Mittag-Leffler function, Generalized Wright hypergeometric function, Mathematics, QA1-939
33 references, page 1 of 3

1. J. Choi and D. Kumar, Certain uni ed fractional integrals and derivatives for a product of Aleph function and a general class of multivariable polynomials, Journal of Inequalities and Applications, 2014 (2014), 15 pages.

2. A. Erdelyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi, Tables of Integral Transforms, McGraw-Hill, New York, 1, 1954.

3. A. Gupta and C.L. Parihar, Fractional di erintegral operators of the generalized Mittag-Le er function, Bol. Soc. Paran. Math., 33(1) (2015), 137{144.

4. H.J. Haubold, A.M. Mathai, and R.K. Saxena, Mittag-Le er functions and their applications, J. Appl. Math. (Article ID 298628) (2011), 1{51.

5. A.A. Kilbas and M. Saigo, Fractional integrals and derivatives of Mittag-Le er type function, Doklady Akad. Nauk Belarusi, 39(4) (1995), 22{26.

6. A.A. Kilbas, M. Saigo and R.K. Saxena, Generalized Mittag-Le er function and generalized fractional calculus operators, Integral Transform Special Function, 15 (2004), 31{49. [OpenAIRE]

7. A.A. Kilbas, M. Saigo and J.J. Trujillo, On the generalized Wright function, Fract. Calc. Appl. Anal., 5(4) (2002), 437460.

8. Y.C. Kim, K.S. Lee and H.M. Srivastava, Some applications of fractional integral operators and Ruscheweyh derivatives, J. Math. And. Appl., 197(2) (1996), 505- 517.

9. V. Kiryakova, All the special functions are fractional di erintegrals of elementary functions, Journal of Physics A: Mathematical and General, 30(14) (1997), 5085- 5103. [OpenAIRE]

10. D. Kumar and J. Daiya, Fractional calculus pertaining to generalized Hfunctions, Global Journal of Science Frontier Research: F Mathematics and Decision Sciences, 14(3) (2014), 25{36.

11. D. Kumar and S. Kumar, Fractional Calculus of the Generalized Mittag-Le er Type Function, International Scholarly Research Notices 2014 (2014), Article ID 907432, 6 pages.

12. D. Kumar and S.D. Purohit, Fractional di erintegral operators of the generalized Mittag-Le er type function, Malaya J. Mat., 2(4) (2014), 419{425.

13. D. Kumar and R.K. Saxena, Generalized fractional calculus of the M -Series involving F3 hypergeometric function, Sohag J. Math., 2(1) (2015), 17{22.

14. O.I. Marichev, Volterra equation of Mellin convolution type with a Horn function in the kernel, Izvestiya Akademii Nauk BSSR. Seriya Fiziko-Matematicheskikh Nauk, 1 (1974), 128-129, (Russian).

15. A.M. Mathai and H.J. Haubold, Special Functions for Applied Scientists, Springer, New York, 2008.

33 references, page 1 of 3
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue