Generalization of Fourier and Mellin transforms

Abstract

Integral transform, such as Fourier and Mellin are helpful in providing techniques for solving problems in differential equations. It can be used as a mathematical tool to solve these problems. In this paper, we find the correlation of Fourier transform and Mellin transforms of some function f:R→C and characterizing condition in terms of Mellin transform. This will not only be helpful in solving various differential and integral equations, but also have versatile applications in many fields of applied science.