Explicit solutions to some fragmentation equations with growth or decay

TL;DR

This paper develops a systematic method for deriving explicit solutions to certain continuous fragmentation equations that include growth or decay terms, focusing on constant and linear coefficient cases.

Contribution

It introduces a new systematic approach for explicitly solving fragmentation equations with growth or decay, covering constant and linear coefficient scenarios.

Findings

Explicit solutions for constant growth/decay coefficients

Explicit solutions for linear growth/decay coefficients

Method applicable to a class of fragmentation equations

Abstract

In this paper, we provide a systematic way of finding explicit solutions for a class of continuous fragmentation equations with growth or decay in the state space and derive explicit solutions in the cases of constant and linear growth/decay coefficients.