Integral transforms of the S-functions

Abstract

The object of this paper is to introduce a new special function, which will be called S-function. This function is an extension of the generalized Mittag-Leffler function due to Prabhakar [7], generalized Mittag-Leffler function introduced by Srivastava and Tomovski [14] and M-series given by Sharma and Jain [13], various integral transform of this function such as Euler transform, Laplace transform, Whittaker transform, K-transform are derived. The results obtained are useful in applied problems of science, engineering and technology.

Keywords

• Euler transform
• Laplace transform
• Whittaker transform
• fractional Fourier transform
• generalized k-Mittag-Leffler function
• generalized Wright function