Some Relations on the Double \(\mathcal {L}_{22}\)-Integral Transform and Their Applications

In this paper, the authors introduce the double Laplace-type integral transform \({\mathcal {L}}_{22}\) and its properties. Several simple theorems dealing with general properties of the \({\mathcal {L}}_{22}\)-integral transform are proved. The convolution, its properties and convolution theorem are given. The main focus of this paper is to develop a method for the \({\mathcal {L}}_{22}\)-integral transform to solve problems in applied mathematics which involve partial differential and integral equations.