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

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.