Boudabsa, LotfiSimon, ThomasVallois, Pierre2020-10-212020-10-212020-10-212020-01-0110.1214/20-EJP520https://infoscience.epfl.ch/handle/20.500.14299/172645WOS:000575514400001We consider three classes of linear differential equations on distribution functions, with a fractional order alpha is an element of [0; 1]. The integer case alpha = 1 corresponds to the three classical extreme families. In general, we show that there is a unique distribution function solving these equations, whose underlying random variable is expressed in terms of an exponential random variable and an integral transform of an independent alpha-stable subordinator. From the analytical viewpoint, this distribution is in one-to-one correspondence with a Kilbas-Saigo function for the Weibull and Frechet cases, and with a Le Roy function for the Gumbel case.Statistics & ProbabilityMathematicsdouble gamma functionextreme distributionfractional differential equationkilbas-saigo functionle roy functionstable subordinatorlawtext::journal::journal article::research article