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.

Inverse Problems for a Conformable Fractional Diffusion Operator

“…In 2017, Jarad et al [15] showed that this derivative is necessary and useful for generating new types of fractional operators. In recent years, numerous significant studies [16][17][18][19][20] have been conducted on inverse problems related to various conformable fractional operators, including the diffusion operator.…”