In this paper, a second order differential pencil, namely diffusion equation with Dirichlet boundary conditions which includes conformable fractional derivatives of order $\alpha (0<\alpha \le 1)$ 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.

在本文中，一个二阶微分铅笔，即具有 Dirichlet 边界条件的扩散方程，其中包括阶次的可整合分数阶导数 $\alpha (0<\alpha \le 1)$而不是传统扩散算子中的普通导数，被考虑。首先得到算子的特征值和特征函数的渐近公式。其次，研究了作为算子本征函数零点的节点。随后，给出了求解逆节点问题的有效程序，从而借助节点的密集子集重建了扩散算子的势。最后，通过一个例子来说明本研究的理论发现。