Evaluating Complex Inverse Formulas for q-Sumudu Transforms

Abstract

In this paper, q-analogues of the Sumudu transform, along with an inversion formula and some explicit computations, are presented. This work essentially focuses on q-analogues of the inverse Sumudu transform and the construction method of the inversion formula via a path integral along a Bromwich contour. It is also shown how the complex inversion formulas considered in this paper admit q-expansions that yield various inverse q- Sumudu transforms for q-series.