Inverse Problems for a Conformable Fractional Diffusion Operator

In this paper, we consider a diffusion operator with discrete boundary conditions, which include the conformable fractional derivatives of order $\alpha$ such that $0<\alpha\leq1$ instead of the ordinary derivatives in the classical diffusion operator. We prove that the coefficients of the given operator are uniquely determined by the Weyl function and spectral data, which consist of a spectrum and normalizing numbers. Moreover, using the well-known Hadamard's factorization theorem, we prove that the characteristic function $\Delta_{\alpha}\left(\rho\right)$ is determined by the specification of its zeros for each fixed $\alpha$. The obtained results in this paper can be regarded as partial $\alpha$-generalizations of similar findings obtained for the classical diffusion operator.