There is quite some, eg https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3106288/ . I believe at least some of the pathways are shared with exercise as well so exercising and/or exercising while fasting would be expected to compound the effect.

edit: sjcsjc beat me to it with the same link

Here's one: "Short term fasting induces profound neuronal autophagy" http://www.tandfonline.com/doi/full/10.4161/auto.6.6.12376