Inverse problem for determining the order of fractional derivative in mixed-type equations

TL;DR

This paper addresses the inverse problem of identifying fractional derivative orders in mixed-type equations combining subdiffusion and wave equations, providing conditions for unique determination of these parameters.

Contribution

It introduces a method to uniquely determine unknown fractional orders in mixed-type equations with different fractional derivatives in different parts of the domain.

Findings

Derived conditions for unique parameter identification

Extended inverse problem theory to mixed-type fractional equations

Applicable to N-dimensional domains

Abstract

In this paper the inverse problem of determining the fractional orders in mixed-type equations is considered. In one part of the domain the considered equation is the subdiffusion equation with a fractional derivative in the sense of Gerasimov-Caputo of the order 0<a<1 , and in the other part - a wave equation with a fractional derivative of the order 1<b<2 . The elliptic part of the equation is a second-order operator, considered in a N - dimensional domain D. Assuming the parameters a and b to be unknown, additional conditions are found that provide an unambiguous determination of the required parameters.