Reconstruction of an initial function from the solutions of the fractional wave equation on the light cone trace

Abstract

We reconstruct the initial functions from the trace of the solution of an initial value problem for the wave equation on the light cone. A method to recover the initial function from the solution of the wave equation on the light cone is already known for odd spatial dimensions. We generalize their work to the fractional wave equation and all dimensions. In other words, we present a method to reconstruct the initial functions from the solution of the fractional wave equation on the light cone.