A GENERALIZATION OF LAPLACE AND FOURIER TRANSFORMS | Asian Journal of Mathematics and Computer

In this note, we suggest a symmetric Laplace transform, which is a generalisation of the Laplace and Fourier transforms. It incorporates the benefits of both the Fourier and the Laplace transforms. We provide a specification for this generalisation, as well as several examples and fundamental features. Using the theory of the Fourier transform, we can also determine the shape of its inverse. Finally, the symmetric Laplace transform is applied to a parabolic issue as well as an ordinary differential equation.

Please see the link :- https://www.ikprress.org/index.php/AJOMCOR/article/view/1004