The third law of thermodynamics and the fractional entropies

•The third law is applied as a test for the fractal calculus based entropies.•Ubriaco entropy is found to conform to the third law.•Machado entropy fails the third law.•The results are supported by 1D Ising model with zero external field.

We consider the fractal calculus based Ubriaco and Machado entropies and investigate whether they conform to the third law of thermodynamics. The Ubriaco entropy satisfies the third law of thermodynamics in the interval 0