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We use the q-Weibull distribution and define a new counting process using the fractional order. As a consequence, we introduce a q-process with q-Weibull interarrival times. Some interesting special cases are also discussed which leads to a Mittag-Leffler form

international journal of stochastic analysis

A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-Weibull Counting Process through a Fractional Differential Operator

A q-Weibull Counting Process through a Fractional Differential Operator