• APPLICATION OF THE MELLIN TYPE INTEGRAL TRANSFORM IN THE RANGE [0, 1/a]

In this paper Laplace operators are used to solve the Mellin Type Integral Transform which can be a technique for solving boundary and initial value problems. This Transforms is applicable in finite interval. This work intends to understand how Laplace operators leads to properties and relations with the Mellin Type Integral Transform. The main aim of this work is to find the relation between Laplace transform and the Mellin Type Integral Transform in [0,1/a], the result have been modified by applying suitable functions which leads to the results of Mellin Type Integral Transform in the interval 0≤t≤1/a. We illustrate the advantages and use of this transformation Cauchy’s Differential Equation have been solved. We have also studied graphical representation of Mellin Type Integral Transform using MATLAB.