Several of Southwest Airlines’ competitors will place price caps on travel to help the thousands of passengers stranded by the budget carrier’s mass flight cancellations this week. This news comes as the embattled air company said it planned to operate one-third of its schedule on Thursday 29 December but then “to return to normal operations with minimal disruptions on Friday” 30 December.

American Airlines and United will implement a ceiling on air fares between certain cities, according to CNN. Delta has implemented “walk-up fare caps in US domestic markets”, a spokesperson for the carrier told Axios.

Alaska Airlines, which told Axios that it already had price ceilings in place, will also cut fares in certain cities. Frontier Airlines reportedly said that it limited its top fares to “pre-disruption levels”. Spirit, meanwhile, was waving “modification changes or fare difference” between dozens of cities through 3 January, the news outlet said.

Southwest has axed 2,357 flights on Thursday, far eclipsing any other carrier, data from Flightaware.com indicates. On Wednesday, Southwest cancellations reached 2,510. Federal authorities said they would investigate the transit meltdown.

Southwest’s descent into logistical chaos started on Thursday 22 December. While many airlines saw cancellations due to a historic winter storm that brought blizzard-like conditions to much of the US, Southwest cancelled numerous flights in areas such as southern California that were not reeling from inclement weather.

The cancellations waylaid thousands of flyers over the holiday weekend and into this week, with no clear path for returning home. There were numerous accounts of hours-long lines, days-long delays, overflowing baggage claims and teary Southwest agents who were contending with livid customers.

Southwest’s rebooking policy worsened the company’s customers’ plight. The airline does not rebook passengers on competing airlines, according to CNN.

As Southwest does not have agreements with other carriers that would permit rebooking on rival airlines, this limits customers’ options. “Southwest is unique in the industry in that we don’t have codeshare partners,” a Southwest spokesperson told CNN. “That is just part of our business model.”

“I’m truly sorry,” Southwest’s chief executive, Bob Jordan, said in a video on Tuesday. He blamed cancellations on cold temperatures across the US, claiming they affected flight paths. “[A]fter days of trying to operate as much of our full schedule across the busy holiday weekend, we reached a decision point to significantly reduce our flying to catch up.”

Asked for comment on its rivals’ initiatives, Southwest told the Guardian in an email this morning: “We can’t comment on other airlines.”

“We continue to operate a reduced schedule by flying roughly one-third of our schedule through Thursday, as of now. We have no updates or adjustments to share regarding Friday’s schedule,” the company said. “Our teams are continuing the work of reuniting customers with their bags.”

Southwest said it stood up additional resources to aid customers in the form of webpages to locate luggage and information on where they can contact Southwest torebook or request a refund.

The airline said later on Thursday that it believed it could “return to normal operations” on Friday after one more day of running one-third of its schedule.

The US transportation secretary, Pete Buttigieg, has said the federal transit agency would investigate Southwest’s mass cancellations and determine whether it was meeting its legal obligations to affected customers. Buttigieg said that Southwest at a minimum should pay cash refunds for cancelled flights, as well as pay for passengers’ lodging and food costs.

“While we all understand that you can’t control the weather, this has clearly crossed the line from what is an uncontrollable weather situation to something that is the airline’s direct responsibility,” Buttigieg recently said on NBC Nightly News.

The US Senate’s commerce committee chairperson, Maria Cantwell, also vowed to conduct an investigation. Two of Cantwell’s fellow Democratic senators and commerce committee members have also demanded that Southwest give “significant” compensation to marooned customers, insisting that the carrier is capable of doing so if its plans to dole out $428m in dividends this January is any indication.

While the pandemonium at Southwest caused widespread misery, some passengers who were left stuck managed to find a way home together. Some hapless travelers – who were strangers to each other – banded together on road trips rather than wait out the airline.

Bridget Schuster, one of these road-trippers, went on TikTok and documented her journey from Florida to Ohio with three other passengers, all initially strangers.

“So far, no serial killer vibes,” Schuster quipped.

The Associated Press contributed reporting