Integral transformations have been successfully used for almost two centuries in solving many problems in applied mathematics, mathematical physics, engineering and technology. The origin of the integral transforms is the Fourier and Laplace transforms. Integral transformation is one of the well known techniques used for function transformation. Integral transform methods have proved to be of great importance in initial and boundary value problems of partial differential equation. The Fourier as well as Laplace transforms have various applications in various fields like science, physics, mathematics, engineering, geophysics, medical, cellular phones, electronics and many more as we have seen in earlier papers. In this paper we discussed about Fourier-Laplace transforms and this Fourier-Laplace transform may also have many applications in various fields.
This paper presents the generalization of Fourier-Laplace transform in distributional sense. Testing function spaces are defined, also some Abelian theorems of the initial and final value type are given. And the Abelian theorems are of considerable importance in solving boundary value problems of mathematical physics.