I tried for a few minutes but I couldn't find what these alleged fragments say? So the evidence at this point in this thread says there is no contemporary writings about Alexander the Great, the man whom history says conquered much of the world and even the Holy Land. Why no contemporary sources for such a great world conqueror??
Please stop reading apologetic evangelical websites that spout nonsense about how Jesus is better attested that Alexander or Caesar in the historical record. It's not difficult to find out what the "alleged fragments" say. Here are some. What they say makes sense, by the way.
http://www.livius.org/aj-al/alexander/alexander_z1.html In the summer of 330, the Athenian politician Aeschines attacked his rival Demosthenes for the failure of the latter's anti-Macedonian policy. His speech is known as Against Ctesiphon. It has survived in copies.
What strange and unexpected event has not occurred in our time? ... the unfortunate Spartans, who were only involved with these events at the beginning when the temple at Delphi was captured, and who at one time claimed to be the leaders of the Greeks, are now about to be sent to Alexander as hostages to parade their misfortune.
Here are a couple of notices whose originals survive from Alexander's day. Public inscription:
From King Alexander to the people of [the Greek island of] Chios, written in the prytany of Deisitheos: [probably 334/3 BC] All those exiled from Chios are to return, and the constitution on Chios is to be democratic. Drafters of legislation are to be selected to write and emend the laws ... Anything already emended or drafted is to be referred to Alexander.
http://www.livius.org/aj-al/alexander/alexander_t40.html From a cuneiform tablet found in a temple in Babylon, containing notes of contemporary astronomical observations, and other current events
On the eleventh, in Sippar an order of Al[exander to the Babylonians was sent as follow]s: 'Into your houses I shall not enter.' [12] On the thirteenth, [the vanguard advanced to the Sikil]la gate, to the outer gate of Esagila and [the Babylonians prostrated themselves]. Alexander, king of the world, came into Babylon [lacuna], horses and equipment of [lacuna] and the Babylonians and the people of [lacuna] a message to ...
We are told by trustworthy historians that earlier writers, whose works are lost, mentioned Alexander, as we might expect. We KNOW that writers contemporary with Jesus, if he existed, or who were active later in the first century, did NOT mention him. (I reject the Josephus references as spurious.) But nothing in Philo, nothing in Justus, nothing in Pliny the Elder. The notices we do have, from Pliny the Younger, Suetonius and Tacitus in the early second century, refer to Christian communities, which we know existed by that time. They never name Jesus.
When references to Jesus do start to appear, they are full of supernatural nonsense about a divine miracle worker. We have stuff like that about Alexander too, but nobody believes a word of it!