Mithun, 24, made his Twenty20 debut against Sri Lanka at Chittagong in February, but was not selected for the subsequent Asia Cup and the World T20 tournaments.
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Spotted as one of the quickest bowlers in Bangladesh, Taskin, 19, made his T20 debut against Australia in the World Cup. The youngster made heads turn when he clean bowled Glenn Maxwell for 5.
Meanwhile, Bangladesh's highest wicket-taker in 2013-14 domestic season, medium-pacer Rubel Hossian, was left out of the squad with bowling all-rounder Ziaur Rahman given preference.
Imrul Kayes, Arafat Sunny, Naeem Islam and Shafiul Islam, who were part of the Asia Cup ODI squad, have also been excluded, while Tamim Iqbal returned to the squad after missing the five-nation tournament due to a neck injury.
Chief selector Faruque Ahmed said Mithun and Taskin had been included to test Bangladesh's bench strength ahead of the 2015 World Cup.
"We have kept more or less a settled squad but it is also important to get an idea about the kind of back up we have in our hands as we start preparing for the World Cup in Australia and New Zealand," Faruque said.
"Mithun (Ali) has been under our radar for a while. He has performed consistently in the limited overs format and in the longer version as well during the last couple of years and deserves a chance at international level.
"Taskin (Ahmed) is an exciting prospect and has already played a Twenty20 international. We thought it was a good opportunity to see how he performs in the 50-over game in home conditions against some quality batsmen," Faruque insisted.
He also explained that the omission of Rubel and justified the selection of medium pacer Al-Amin Hossain and off-spinning all-rounder Mahmudullah.
"Al Amin has bowled impressively since his debut and Mashrafe Mortaza is our most experienced campaigner. We also have a seam-bowling all-rounder in Ziaur Rahman. Because of these pace options and squad balance Rubel Hossain misses out.
The spin department is well covered with Abdur Razzak, Shakib
Al Hasan and Sohag Gazi. Mahmudullah is also quite handy and can do a job for his captain," said Faruque.
Squad: Mushfiqur Rahim (capt), Tamim Iqbal, Anamul Haque, Shamsur Rahman, Mominul Haque, Shakib Al Hasan, Nasir Hossain, Mahmudullah, Mithun Ali, Abdur Razzak, Mashrafe Mortaza, Sohag Gazi, Ziaur Rahman, Al-Amin Hossain, Taskin Ahmed.
Image: Taskin Ahmed of Bangladesh celebrates after dismissing Glenn Maxwell of Australia during the ICC World Twenty20 Bangladesh 2014.
Photograph: Scott Barbour/Getty Images