Identification of the Order of the Fractional Derivative for the Fractional Wave Equation

Abstract

A fractional wave equation with a fractional Riemann–Liouville derivative is considered. An arbitrary self-adjoint operator A with a discrete spectrum was taken as the elliptic part. We studied the inverse problem of determining the order of the fractional time derivative. By setting the value of the projection of the solution onto the first eigenfunction at a fixed point in time as an additional condition, the order of the derivative was uniquely restored. The abstract operator A allows us to include many models. Several examples of operator A are discussed at the end of the article.