Generalized fractional calculus and some models of generalized counting processes

Abstract

Models of generalized counting processes time-changed by a general inverse subordinator are considered, their distributions are characterized, and governing equations for them are presented. The equations are given in terms of the generalized fractional derivatives, namely, convolution-type derivatives with respect to Bernštein functions. Some particular examples are presented.

Keywords

• Time-change
• Poisson process
• generalized counting process
• subordinator
• inverse subordinator
• generalized fractional derivatives