Although it is not fully proven that these types of diets can help reduce the risk of cognitive-decline related health issues, evidence does suggest that it can reduce risk of cognitive decline.

Find some of this evidence, gathered by the National Institute of Aging below:

• In an observational study of 116 cognitively normal adults, those who followed a Mediterranean diet had thicker cortical brain regions than those who did not. It seems that these regions shrink in people with Alzheimer’s, so thicker regions could mean cognitive benefit. 
• An analysis of diet and other factors found that, after an average of 4.5 years, people who closely followed MIND diet had a 53% reduced rate of Alzheimer’s disease compared to those who did not follow the diet closely.
• In a similar study, following the MIND diet was associated with a substantial slowing of cognitive decline during an average of almost 5 years