Copyright © 2011 Kunnummal Muralidharan and Seema S. Nair. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We use the -Weibull distribution and define a new counting process using the fractional order. As a consequence, we introduce a -process with -Weibull interarrival times. Some interesting special cases are also discussed which leads to a Mittag-Leffler form.