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Arthur Wellesley was an aristocratic character in the novel Commodore Hornblower. He was the brother of Barbara Wellesley and the brother-in-law of Horatio Hornblower. Wellesley commanded the British army in Spain, fighting the forces of Napoléon Bonaparte. (DS9: "The Visitor")

The character is based on Arthur Wellesley, 1st Duke of Wellington, who defeated Napoléon in the battle of Waterloo and for whom Wellington, New Zealand, was named after.
The section of text seen on the PADD does not give a name to Barbara's brother. The name of her brother comes from the article at Wikipedia about Horatio Hornblower.