Some properties of a new general triple complex integral transform

This paper investigates a novel triple complex integral transform, highlighting its properties and its applications to functional, integral, and partial differential equations. Several fundamental theorems describing the general characteristics of the triple complex integral transform are formulated and rigorously proved. The concept of convolution associated with the transform is also examined, its properties are established, and a detailed proof of the convolution theorem is presented. Integral transformations are regarded as one of the most important methods for solving partial differential equations, as they often simplify both the solution procedure and the underlying mathematical operations. In particular, higher-order partial differential equations admit simpler solutions in the framework of integral transforms. The triple complex transform considered in this work (Complex Sadik triple integral transform) is likewise shown, through illustrative examples, to yield simpler solution steps compared with previous methods. The central objective of this study is to develop the triple complex integral transform as an effective tool for solving initial and boundary value problems in applied mathematics and mathematical physics.