Beyond Laplace and Fourier transforms: Challenges and future prospects

This is the authors' abstract. We don't add key points for this paper.

Laplace and Fourier transforms are widely used independently in engineering for linear differential equations including fractional differential equations. Here we introduce a generalized integral transform, which is a generalization of the Fourier transform, Laplace transform, and other transforms, e.g., Sumudu transform, Aboodh transform, Pourreza transform, and Mohand transform, making the new transform much attractive and promising. Its basic properties are elucidated, and its applications to initial value problems and integral equations are illustrated, when coupled with the homotopy perturbation, it can be used for various non-linear problems, opening a new window for non-linear science.