Oh wait what? Stable no. Prosperous yes, for themselves maybe but nobody else.
Islam invaded the Caucasus (Persia) via Muslim expansion into the Caucasus in the 7th century and the Umayyad conquest of Iberia after that meant that much of the Iberian Peninsula was occupied until the 15th century. The Ottoman Empire also conquered and occupied the Balkans and remnants of the Byzantine Empire. After stalling at the Gates of Vienna in 1529, the Ottoman Empire then declined, until it was defeated and eventually collapsed, relatively recently. in 1922. All of these invasions and occupations featured multiple battles, deaths, significant slavery and instability.