A New Family of Fractional Renewal Processes

TL;DR

This paper introduces a novel family of fractional renewal processes using a new generalized density concept, expanding the theoretical framework beyond existing fractional renewal models.

Contribution

It presents a new approach to constructing fractional renewal processes in the alpha-fractional space, offering a fresh generalization of the Poisson process.

Findings

New fractional renewal processes in alpha-fractional space

Demonstrates usefulness as a generalization of Poisson process

Introduces a generalized density function concept

Abstract

Fractional renewal processes as a generalization of Poisson process are already in the literature. In this paper, by introducing a new concept of generalized density function, the authors construct new fractional renewal processes in the $\alpha$-fractional space and show that it is another interesting and useful generalization of Poisson process.