Inverse Problem for Determining the Order of the Fractional Derivative in Mixed-Type Equations

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 $$\alpha\in(0,1)$$ and in the other part—a wave equation with a fractional derivative of the order $$\beta\in(1,2)$$ . The elliptic part of the equation is a second-order operator, considered in $$N$$ -dimensional domain $$\Omega$$ . Assuming the parameters $$\alpha$$ and $$\beta$$ to be unknown, additional conditions are found that provide an unambiguous determination of the required parameters.

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