The extended Mittag-Leffler function via fractional calculus
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Authors
Gauhar Rahman
- Department of Mathematics, International Islamic University, Islamabad, Pakistan.
Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey.
- Institute of Space Sciences, Magurele-Bucharest, Romania.
Maysaa Al Qurashi
- Department of Mathematics, College of Science, King Saud University, Riyadh, Saudia Arabia.
Sunil Dutt Purohit
- Department of HEAS (Mathematics), Rajasthan Technical University, Kota, India.
Shahid Mubeen
- Department of Mathematics, University of Sargodha, Sargodha, Pakistan.
Muhammad Arshad
- Department of Mathematics, International Islamic University, Islamabad, Pakistan.
Abstract
In this study, our main attempt is to introduce fractional calculus (fractional integral and differential) operators which contain the following new family of extended Mittag-Leffler function:
\[
E_{\alpha,\beta}^{\gamma;q, c}(z)=\sum\limits_{n=0}^{\infty}\frac{B_p(\gamma+nq, c-\gamma)(c)_{nq}}{B(\gamma, c-\gamma)\Gamma(\alpha n+\beta)}\frac{z^n}{n!},~~~ (z,\beta, \gamma\in\mathbb{C}),
\]
as its kernel. We also investigate a certain number of their consequences containing the said function in their kernels.
Share and Cite
ISRP Style
Gauhar Rahman, Dumitru Baleanu, Maysaa Al Qurashi, Sunil Dutt Purohit, Shahid Mubeen, Muhammad Arshad, The extended Mittag-Leffler function via fractional calculus, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 8, 4244--4253
AMA Style
Rahman Gauhar, Baleanu Dumitru, Qurashi Maysaa Al, Purohit Sunil Dutt, Mubeen Shahid, Arshad Muhammad, The extended Mittag-Leffler function via fractional calculus. J. Nonlinear Sci. Appl. (2017); 10(8):4244--4253
Chicago/Turabian Style
Rahman, Gauhar, Baleanu, Dumitru, Qurashi, Maysaa Al, Purohit, Sunil Dutt, Mubeen, Shahid, Arshad, Muhammad. "The extended Mittag-Leffler function via fractional calculus." Journal of Nonlinear Sciences and Applications, 10, no. 8 (2017): 4244--4253
Keywords
- Fractional integration
- differential operator
- Mittag-Leffler function
- Lebesgue measurable function
- extended Mittag-Leffler function.
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