An Analog of the Tricomi Problem for a Mixed-Type Equation with Fractional Derivative. Inverse Problems

In this paper, an analog of the Tricomi problem for a mixed-type equation with a fractional derivative is studied. In one part of the domain, the considered equation is a subdiffusion equation with a fractional derivative of order $$\alpha\in(0,1)$$ in the sense of Riemann–Liouville, and in the other part, it is a wave equation. Two types of inverse problems are considered. Assuming parameter $$\alpha$$ to be unknown, the corresponding inverse problem is studied and an additional condition is found that provides a unique definition of the sought-for parameter. Then, assuming the boundary value of the solution to be unknown, an additional condition is defined that ensures the existence and uniqueness of the unknown value of the solution.

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