"Why post 1900? With a medieval pod it would be easy." Thats why is a challenge. Have a great majority of africa be muslim.
So they pull a Gaddafi?Ottoman Empire holds together long enough to find all that oil and finances revolutions throughout Africa to undermine those who had abused the "sick man" for decades. Islam becomes intertwined with anticolonialism and...there we go.
How do the Ottomans expand into Italian Eritrea and Somaliland with their tenuous control over Southern Arabia?In WW1, the Ottomans expand at Italy's expense. They gain Eritrea and Italian Somaliland. They also conquer Chad from France.