Fractional Laplace Transforms - A Perspective

TL;DR

This paper reviews a class of fractional Laplace transforms, discussing their properties and potential applications in solving differential equations and problems in non-extensive statistical mechanics.

Contribution

It introduces a perspective on fractional Laplace transforms as a broad class of transforms with useful properties for applied mathematics and physics.

Findings

Properties of fractional Laplace transforms are systematically discussed.

Potential applications in differential equations are highlighted.

Relevance to non-extensive statistical mechanics is explored.

Abstract

A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral equations or problems in non-extensive statistical mechanics.