Cell Division And The Pantograph Equation

Abstract

Simple models for size structured cell populations undergoing growth and division produce a class of functional ordinary differential equations, called pantograph equations, that describe the long time asymptotics of the cell number density. Pantograph equations arise in a number of applications outside this model and, as a result, have been studied heavily over the last five decades. In this paper we review and survey the rôle of the pantograph equation in the context of cell division. In addition, for a simple case we present a method of solution based on the Mellin transform and establish uniqueness directly from the transform equation.Article published online by EDP Sciences and available at https://www.esaim-proc.org or https://doi.

An advection-diffusion process with proportional resetting

“…of overhead power delivery wires for electric trains (i.e., pantograph wires) [46,47]. Analogues of ( 5) have been used in biophysics to model the size distribution of a population of dividing cells [48][49][50]. Other contexts for pantograph-type functional equations are discussed in [51,52].…”

On Pantograph Problems Involving Weighted Caputo Fractional Operators with Respect to Another Function

“…A pantograph is essentially a measuring and drawing tool. Currently, electric trains and electric cells employ this device [24][25][26]. In 1971, Ockendon and Taylor [27] investigated what is now known as PE, or how electric flow is collected by the pantograph of an electric train.…”

Stability analysis for a tripled system of fractional pantograph differential equations with nonlocal conditions

“…Kilbas et al (2006); Rekhviashvili et al (2019); Miller and Ross (1993); Lakshmikantham et al (2009); Hedayati et al (2021); Noeiaghdam et al (2021a,b). Moreover, it has been used to simulate physical, technical processes are best characterized by fractional differential equations (see Ahmad and Nieto (2009); Abdeljawad and Samei (2021); Brunt et al (2018); Hammad et al (2021) and references therein). Also, the stability of fractional order differential equation is an important and useful part of fractional differential equations and it has been introduced in several works Alzabut et al (2021); Hyers (1941); Jung (2006); Rus (2010); Rassias (2000); Hajiseyedazizi et al (2021); Ahmad et al (2020); Tang et al (2016); Shah and Tunc (2017); Kaabar et al (2021); Kalvandi et al (2019); Selvam et al (2022); Deepa et al (2022).…”