Properties of \(k\)-Riemann-Liouville fractional integral operator with Mittag-Leffler functions. (English) Zbl 1524.33082
Summary: In this paper, we will introduce some properties based on the Laplace transform and Millen transform for \(k\)-Riemann Liouville fractional integral operator involving the Mittag-Leffler functions. The Laplace transform and Millen transform of \(k\)-Riemann Liouville operator will be obtained and also new interesting results will be introduced by the help of properties of the Mittag-Leer function.
MSC:
| 33E12 | Mittag-Leffler functions and generalizations |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
References:
| [1] | Bapna I.B. and Jain N. (2008), Application of modied fractional calculus ap-plied in statistical distribution, Math. Sci. res. J., vol. 12(11), pp. 258-269 · Zbl 1182.26006 |
| [2] | Bapna, I.B. and Mathur, N., (2012),application of fractional calculus in statis-tics, International Journal Contemporary Mathematical science, vol. 7, no. 18, pp.849-856 · Zbl 1248.62028 |
| [3] | Haubold, H., J., Mathai M. A. and Saxena, R.K. (2011),Mittag Leer Func-tions and their Applications, Hindawi Publishing Corporation Journal of applied mathematics vol. 2011 Article ID298628, 51 pages · Zbl 1218.33021 |
| [4] | Mittag-Leer,S.G.(1903) Sur la function,C.R Acad. Sci. Paris,No.137 pp 554-558 |
| [5] | Mubeen S., and Habibullah G.,M.(2012), k-fractional integral and applications, International Journal Contemporary Mathematical Science, vol. 7, pp.89-94 · Zbl 1248.33005 |
| [6] | Mathai , A., and Haubold, H.(2008), Special function for applied scientists, Springer · Zbl 1151.33001 |
| [7] | Prabhakar, T.R.(1971), A singular integral equation with a generalized Mittag-Leer function in the kernel, Yokohama Math. J., No. 19, pp.715 |
| [8] | Salim T.O., (2009), Some properties relating to the generalized Mittag-Leer function. Adv Appl Math Anal 4: 2130 |
| [9] | Shukla, A.K. and Prajapati, J.C.(2007), On a generalization of Mittag-Leer function and its properties, J. Math. Anal. Appl. No 336 (2007), 797-811. · Zbl 1122.33017 |
| [10] | Romero,L.G, Luciano L. Luque, L.,Dorrego G.A., and Cerutti ,R.A,(2013), On the k-Riemann-Liouville Fractional Derivative, Int. J. Contemp. Math. Sci-ences,Vol. 8, no. 1, 41 -51, · Zbl 1285.26009 |
| [11] | Wiman, A. Uber den fundamental satz in der theory functionen, Acta Math.,No.29, pp 191-201 · JFM 36.0471.01 |
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