Is there a relation between Asperger and Alzheimer's?

Not known. If you mean Asperger syndrome, this is a form of autism characterized by impaired social interaction, and repetitive patterns of behavior. The latter manifestation can be easily confused with other mental disorders, like schizophrenia, and obsessive-compulsive disorder. Alzheimer's is a subtle form of dementia with memory and function loss as the main symptoms.
None. I looked it up through the medical literature and I found none. Both have different presentations of neurobehavioral activities especially when it comes to dementia.