Convolution Structure of Fractional Quaternion Mellin Transform

Abstract

Mellin transform is a basic tool for analyzing the behavior of many important functions in mathematics and mathematical physics. A quaternion is a 4 dimensional number, a generalization of a complex number. Basically it used in image registration. This paper is focus on the new convolution structure of Fractional Quaternion Mellin transform. Also the main properties i.e. associative, distributive, linear, shifting for the convolution of Fractional Quaternion Mellin Transform are proved.