Integral transforms of \(k\)-generalized Mittag-Leffler function \(E_{k,\alpha ,\beta}^{\gamma ,\tau}(z)\). (English) Zbl 1318.33037
Summary: In this paper we study the Euler Transform, Laplace Transform, Whittaker Transform and Fractional Fourier Transform of order \(\alpha, 0<\alpha\leq1\), of the generalized \(k\)-Mittag-Leffler function \(E^\gamma_{k,\alpha,\beta}(z)\). The results obtained are of general character and provide extension of the results given by R. K. Saxena [in: Proceedings of the 3rd annual conference of the Society for Special Functions and their Applications (SSFA), Varanasi, India, March 4–6, 2002. Chennai: Society for Special Functions and their Applications (SSFA). 75–81 (2002; Zbl 1081.33035)].
MSC:
| 33E12 | Mittag-Leffler functions and generalizations |
