We evaluate the eigenvalues of a type of one-dimensional PT-symmetric fractional Schrödinger equation with multiple quantum wells potential profile. By using a finite-difference scheme, we solve the fractional Schrödinger equation and present the algorithm. We study the effects of different parameters on the pairwise coalescence of eigenvalues. We show that by using the mentioned parameters, we can tune the position of the pairwise coalescence of the eigenvalues and the surface area between the two eigenvalues that intersect. An interesting phenomenon is that a small value of the fractionality as much as 0.15 can destroy the pairwise coalescence of eigenvalues and produce a single energy level. We also, consider the Hofstadter butterfly of a PT-symmetric one-dimensional system and show that by increasing the intensity of the potential imaginary part, we can kill the butterfly.

我们评估一类具有多个量子阱势分布的一维PT对称分数分数Schrödinger方程的特征值。通过使用有限差分方案，我们解决了分数薛定ding方程，并提出了该算法。我们研究了不同参数对特征值的成对合并的影响。我们表明，通过使用上述参数，我们可以调整特征值的成对合并的位置以及相交的两个特征值之间的表面积。一个有趣的现象是分数的小值高达0.15可以破坏特征值的成对合并并产生单个能级。我们也，