Saigo Fractional q-Differentiation Operator Involving Generalized q-Mittag–Leffler Function - Mulugeta Dawud Ali; D. L. Suthar (Journal of Mathematics)
The purpose of this study is to obtain the images of the generalized q-analogue of Mittag–Leffler functions under the Saigo fractional q-differentiation operator, where its argument consists of a factor xζxq−μ+ξ−θ. Corresponding assertions in terms of Weyl q-integral operator, Kober q-integral operator, and Riemann–Liouville q-integral operator are presented. We also use the q-Laplace transforms to create their composition formula. In addition, we emphasize their significance in particular.