Operational Calculus of the Sumudu – Finite Mellin Transform

Abstract

The Sumudu–Finite Mellin Transform (SFMT) is a new hybrid integral transform obtained by combining the kernels of the Sumudu transform and the finite Mellin transform. In this paper, the Sumudu-Finite Mellin Transform is introduced and studied in the framework of generalized functions. Suitable testing function spaces are defined using the Gelfand–Shilov technique to establish the distributional form of the transform. Further, important operational properties such as shifting and scaling are obtained. These results extend the theory of hybrid integral transforms and provide a useful analytical tool for solving differential and integral equations over finite domains.