# Fractional Periodic Processes: Properties and an Application of Polymer Form Factors

## TL;DR

This paper introduces three classes of fractional periodic processes, deriving their properties and applying them to ring polymers to obtain analytical expressions for form factors and related quantities.

## Contribution

It provides new analytical formulas for fractional periodic processes and applies them to polymer physics, specifically ring polymers, to understand their form factors.

## Key findings

- Closed-form expressions for form factors and Debye functions.
- Asymptotic decay behavior characterized.
- Relation between end-to-halftime and radius of gyration established.

## Abstract

In this paper we introduce and study three classes of fractional periodic processes. An application to ring polymers is investigated. We obtain a closed analytic expressions for the form factors, the Debye functions and their asymptotic decay. The relation between the end-to-halftime and radius of gyration is computed for these classes of periodic processes.