Fractional Derivative Mittag-Leffler Function Wright Function Renewal Theory Poisson Process Fractional Diffusion 26A33 33E12 33E20 44A10 44A35 60G50 60J05 60K05
Issue Date:
2005
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Fractional Calculus and Applied Analysis, Vol. 8, No 1, (2005), 07p-38p
Abstract:
After sketching the basic principles of renewal theory we discuss the
classical Poisson process and offer two other processes, namely the renewal
process of Mittag-Leffler type and the renewal process of Wright type, so
named by us because special functions of Mittag-Leffler and of Wright type
appear in the definition of the relevant waiting times. We compare these
three processes with each other, furthermore consider corresponding renewal
processes with reward and numerically their long-time behaviour.
