The direct regular flight Moscow-Istanbul is carried out by only 2 companies - this is Aeroflot and Turkish Airlines. If you purchase tickets in advance and follow the booking rules (minimum and maximum length of stay, Sunday rule), you can find a very good tariff.

There are also charter flights, but their policy is such that the ticket price practically does not vary depending on the time and date of departure (the priority of charter flights is not passenger transportation). Again, a number of Baltic and Ukrainian airlines can offer a fairly cheap version of air travel, but it will be a connecting flight.

In season 20 09-year-old airline SkyExpress made it possible to book flights to Istanbul, but the price of tickets sometimes exceeded the current rates of regular airlines

My advice - if you flatly refuse to fly by regular airlines - ask for tickets for charter flights of PanUkraina Airlines or block tickets of others airlines in travel agencies