Ask your airline. For Pegasus, request wheelchair help when you buy the ticket or at least 48 hours before the flight, by calling 0 850 250 67 02 inside Turkey or +90 850 250 67 77 from other countries (Pegasus Help page and General Rules 10.4.2). If you ask for wheelchair help less than 48 hours before the flight, Pegasus says it can only be given if available and may not be on time. Describe what you need, for example that you cannot walk long distances or climb stairs. For a connection, tell the airline that you are changing planes and ask them to confirm that help is arranged for each flight and at the changeover. If your tickets are separate, ask each airline. At the airport where your trip starts, Pegasus says to begin check-in at least 2 hours before departure, and that the help can add time to check-in, boarding and security.
The airport has a help and assistance phone booth next to the disabled entrance on the Departures level. Press 1 for Turkish Airlines or AJet, 2 for Pegasus, and 3 for other airlines. The booth is at the terminal entrance, probably before security, so it is mainly for people who have left the transfer area. If you are inside the transfer area, ask any uniformed staff member or the airline desk. The airport page lists wheelchair service in the international and domestic terminals, staff help from check-in and boarding through security to your seat, accessible toilets, and Braille tablets at all information desks. For wheelchair questions the airport lists PortClinic on +90 216 588 87 80/81 for Pegasus and Airclinic on +90 216 588 22 22 for AJet (the FAQ also lists Airclinic for Turkish Airlines).
The airport page does not say whether wheelchair help is free, how many hours ahead to book, or where the helper meets you. A mobility company says it is free and gives meeting points, but we could not confirm this from the airport or Pegasus. Pegasus rules say that a passenger who cannot manage personal needs such as eating or using the toilet, and who travels without a companion, can be refused carriage, and that cabin crew cannot lift you or help with the toilet. If you need that kind of help, tell the airline about it when you book. The airport shows no electric cart or buggy service, and no free service that is separate from the airline. Paid private meet-and-assist services exist.