The Laplace equation, the heat equation, the wave equation, and the Helmholtz equation in cylindrical or spherical coordinates are just a few of the numerous equations that may be solved using Bessel’s functions in modern engineering and natural science applications. In this paper, we present some important applications for assessing the integration as well as the intricate Sadik integral transform of Bessel’s functions. The efficiency of the complex Sadik integral transform and its ability to provide an accurate solution with the fewest number of calculations are demonstrated using real-world numerical examples.