The Double Laplace Transforms and Their Properties with Applications to Functional, Integral and Partial Differential Equations

Although a very vast and extensive literature including books and papers on the Laplace transform of a function of a single variable, its properties and applications is available, but a very little or no work is available on the double Laplace transform, its properties and applications.This paper deals with the double Laplace transforms and their properties with examples and applications to functional, integral and partial differential equations. Several simple theorems dealing with general properties of the double Laplace transform are proved. The convolution, its properties and convolution theorem with a proof are discussed in some detail. Themain focus of this paper is to develop themethod of the doubleLaplace transform to solve initial and boundary value problems in appliedmathematics, andmathematical physics.