In the 1900 US Census, a Frederick Nelson, born in November 1862 in Illinois. He was a bookkeeper in Topeka, Kansas and listed as married for 16 years (c.1884). However, there is no other family members listed as living with him.
I can't find any link between Frederick J. Nelson and Alice B. Walker.
I'm using Ancestry.com for the research.

Frederick J. Nelson's parents were Frederick Warren Nelson and Susan Carter Nelson. They were married on March 4, 1847 in White County, Ill.