Inverse Nodal Problem for a Conformable Fractional Diffusion Operator With Parameter-Dependent Nonlocal Boundary Condition

Abstract

In this paper, we consider the inverse nodal problem for the conformable fractional diffusion operator with parameter-dependent Bitsadze–Samarskii type nonlocal boundary condition. We obtain the asymptotics for the eigenvalues, the eigenfunctions, and the zeros of the eigenfunctions (called nodal points or nodes) of the considered operator, and provide a constructive procedure for solving the inverse nodal problem, i.e., we reconstruct the potential functions p(x) and q(x) by using a dense subset of the nodal points.