Inverse nodal problem for a conformable fractional diffusion operator

Abstract

In this paper, a second order differential pencil, namely diffusion equation with Dirichlet boundary conditions which includes conformable fractional derivatives of order instead of the ordinary derivatives in a traditional diffusion operator, is considered. Firstly, the asymptotic formulae of eigenvalues and eigenfunctions of the operator are obtained. Secondly, the nodal points which are the zeros of the eigenfunction of the operator are investigated. Later, an effective procedure for solving the inverse nodal problem is given and thus the potentials of the diffusion operator are reconstructed with the help of a dense subset of nodal points. Finally, an example to illustrate the theoretical findings of this study is presented.