Fogle is serving a 15 1/2 year sentence for child porn and traveling to engage in illicit sexual conduct with a child.
The appeal argues Fogle's sentence is unreasonable.
Fogle's attorneys are asking the court to take his medical condition into account.
Fogle faces five to 12.5 years in prison after pleading guilty to child pornography charges.
Ten of the 14 victims have received checks totaling $1 million.
Fogle will pay a total of $1.4 million in restitution to the victims, which breaks down to $100,000 for each of the 14 victims.
Convicted David Bostic filmed children in Monroe County under the age of four in sexually explicit videos he then sent to child predators around the world.
David R. Bostic entered a guilty plea Monday to the sexual exploitation of several Monroe County children between the ages of 2 months and 4 years.