A biomathematical view on the fractional dynamics of cellulose degradation

Abstract

Abstract We perform a biomathematical analysis of a model of cellulose degradation with derivative of fractional order γ. In the theory of biopolymers division, the phenomenon of shattering remains partially unexplained by classical models of clusters’ fragmentation. Thus, we first examine the case where the breakup rate H is independent of the size of the cellulose chain breaking up, following by the case where H is proportional to the size of the cellulose chain. Both cases show that the evolution of the biopolymer sizes distribution is governed by a combination of higher transcendental functions, namely the Mittag-Leffler function, the further generalized G-function and the Pochhammer polynomial. In particular, this shows existence of an eigen-property, that is, the system describing fractional cellulose degradation contains replicated and partially replicated fractional poles, whose effects are given by these functions.