Turkey's high-speed trains (Yüksek Hızlı Tren, YHT) speed between Istanbul and Konya (4 hours 15 minutes, one-way/single fare: TL85 normal, TL142 business class).
Here is the schedule as of May 1, 2018:
Turkish State railways says the number of departures will be increased in the future.
It can be difficult to find the train timetables on the Turkish State Railways website, so I've put them here.
High-speed trains also travel between Istanbul and Eskişehir, Ankara and Konya, Eskişehir and Konya, and Ankara and Eskişehir. More...