The inverse problems about fractional Calder\'on problem and fractional Schr\"odinger equations are of interest in the study of mathematics. In this paper, we propose the inverse problem to simultaneously reconstruct potentials and sources for fractional Schr\"odinger equations with internal source terms. We show the uniqueness for reconstructing the two terms under measurements from two different nonhomogeneous boundary conditions. By introducing the variational Tikhonov regularization functional, numerical method based on conjugate gradient method(CGM) is provided to realize this inverse problem. Numerical experiments are given to gauge the performance of the numerical method.

翻译：分数阶Calderón问题与分数阶薛定谔方程的反问题在数学研究中备受关注。本文针对含内部源项的分数阶薛定谔方程，提出了同时重构势函数与源项的反问题。我们证明了在两种不同非齐次边界条件的测量数据下，这两项参数重构的唯一性。通过引入变分Tikhonov正则化泛函，提出了基于共轭梯度法的数值方法以实现该反问题的求解。数值实验验证了该数值方法的有效性。