Abstract
We investigate a time-dependent Schrödinger-like equation in presence of a nonlocal term by using the method of variable separation and the Green function approach. We analyze the Green function for different forms of the memory kernel and the nonlocal term. Results for delta potential energy function are presented. Distributed order memory kernels are also considered, and the asymptotic behaviors of the Green function are derived by using Tauberian theorem. The obtained results for the Green function for the considered Schrödinger-like equation may be transformed to those for the probability distribution function of a diffusion-like equation with memory kernel and can be used to explain various anomalous diffusive behaviors.
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