Abstract The Laplace transform is a central mathematical tool for analysing 1D/2D signals and the solution to PDEs; however, its definition computation on arbitrary data still an open research problem. We introduce domains focus spectral , which defined by applying 1D filter Laplacian spectrum of input domain. satisfies standard properties 2D transforms, such as dilation, translation, scaling, ...

In this paper we present an extension of Fractional Laplace Transform in the framework non-conformable local fractional derivative. Its main properties are studied and it is applied to resolution differential equations.

In this paper we introduce a generalized Laplace transform in order to work with very general fractional derivative, and obtain the properties of new transform. We also include corresponding convolution inverse formula. particular, definition for improves previous results. Additionally, deal harmonic oscillator equation, showing that its allow one solve differential equations.