New Integral Transform: Fundamental Properties, Investigations and Applications Mr. Kharde Uttam Dattu, Department of Mathematics, S.N.Arts, D.J.M. Commerce & B.N.S. Science College, Sangamner uttamkharde@gmail.com Abstract: Xiao-Jun Yang [1] proposes a new integral Transform called “Yang Transform” and applied to solve Steady Heat Transfer problem. In this paper researcher investigate the fundamental properties of Yang transform and used effectively to solve differential equations with constant coefficients. Also we define Laplace-Yang duality property. Keyword: Integral Transform, New integral transform, linear differential equations, Laplace Transform. 1. INTRODUCTION The differential equation plays a central role in Applied Mathematics, Physics and in Engineering.Linear and Nonlinear Partial differential equations are generally difficult to be solved and their exact solution are difficult to be obtained. The exact solution and numerical solutions of this kind of equations play an important role in physical science and in engineering fields; therefore, there have been attempts to develop new techniques for obtaining analytical solutions which reasonably approximate the exact solutions. In order to solve the differential equations, an integral transforms were extensively used. The importance of an integral transform is that they provide powerful operational methods for solving initial value problems and initial- boundary value problem for linear differential and integral equations.There are several methods like Laplace transform, Fourier transforms, Mellin Transforms, Series Methods, etc are available to solve linear differential equations [2]. In 1993, Watugala G.K. [3] was successfully introducing Sumudu transform to solve differential equations and control Engineering problems. Recently, in 2011 Tariq M. Elzaki introduced new Integral transform “Elzaki Transform” and used heavily in solving ordinary as well as partial differential equations [4-6]. Also in 2013, Khalid Suliman Aboodh introduces “Aboodh Transform” and applies for solving ordinary differential equations [7-8]. It is also used to solve partial differential equations [9], Heat equations [10]. The main objective of this paper is to investigatefundamental properties of newly introduce integral transform called “Yang Transform” discover by Xiao-Jun Yang and was successfully applied to solve Steady-Heat transfer problem [1]. The plan of the paper is as follows: In section 2, we introduce the basic idea of Yang transform, some fundamental properties in 3, then Application to solve ordinary differential equation in 4 and conclusion in 5, respectively. IAE TSD JOURNAL FOR ADVANCE D RE SE ARCH IN APPLIE D SCIE NCE S VOLUME 5, ISSUE 4, APRIL/ 2018 ISSN NO: 2394-8442 http:/ / iaetsdjaras.org/ 534