Inverse problem to determine simultaneously several scalar parameters and a time-dependent source term in a superdiffusion equation involving a multiterm fractional Laplacian

TL;DR

This paper addresses an inverse problem in superdiffusion equations involving multiterm fractional Laplacians, aiming to simultaneously recover multiple parameters and a source term from temporal measurements, with a proof of uniqueness.

Contribution

It introduces a method to uniquely determine scalar parameters, fractional orders, and source terms in a superdiffusion model using Laplace transform asymptotics.

Findings

Proved uniqueness of the inverse problem solution.

Developed a technique based on Laplace transform pole asymptotics.

Established conditions for parameter recovery in superdiffusion equations.

Abstract

Inverse problem to recover simultaneously a scalar coefficient, order of a time-fractional derivative, parameters of multiterm fractional Laplacian and a time-dependent source term occurring in a superdiffusion equation from measurements over the time is considered. Uniqueness of a solution is proved. The proof uses asymptotics of poles of the Laplace transform of a measured function.