Bilateral Laplace-Mellin Integral Transform and its Applications

In this paper we discuss Bi-lateral Laplace-Mellin Integral Transform technique for solving boundary and initial value pr oblems. This Transform is studied in the infinite region (-∞ , 0) to ( ∞ ∞, ). We investigate the properties and theorems li ke inversion theorem, convolution theorem, Parseval's theorem and some properties by using Ramanujan's formula. To illustrate the advantages aof this transformation Cauchy's differential equation have been solved. This work g ives us an insight to understand how this transform can be used for finding the relations wit h other integral transforms. We have also studied graphical representation of Bi-lateral Laplace-Mellin Integral Transform using Matlab.