A Generalization of Integral Transform

Abstract

In this paper, the generalization of integral transform (GIT) of the func-tion G{f (t)} is introduced for solving both differential and interodif-ferential equations. This transform generalizes the integral transformswhich use exponential functions as their kernels and the integral trans-form with polynomial function as a kernel. The generalized integraltransform converts the differential equation in us domain (the trans-formed variables) and reconvert the result by its inverse operator. Inparticular, if u = 1, then the generalized integral transform coincideswith the Laplace transform and this result can be written in anotherform as the polynomial integral transform.