Some sources say that the moment the attack on Carthage took place, Gordian grew desperate, because he knew the power of Maximinus and the lack of any obviously equal force capable of fighting against him in Libya, and hanged himself.
Edition :
Herodian. History of the Empire, Volume I: Books 1-4. Translated by C. R. Whittaker. Loeb Classical Library 454. Cambridge, MA: Harvard University Press, 1969.
Herodian. History of the Empire, Volume II: Books 5-8. Translated by C. R. Whittaker. Loeb Classical Library 455. Cambridge, MA: Harvard University Press, 1970.
Notes :
Herodian depicts an alternative time of death in 7.9.9, where Gordian I. hangs himself only after the battle and the death of his son.