Mathematical Solvability of a Caputo Fractional Polymer Degradation Model Using Further Generalized Functions

The continuous fission equation with derivative of fractional order α, describing the polymerchain degradation, is solved explicitly. We prove that, whether the breakup rate depends on thesize of the chain breaking up or not, the evolution of the polymer sizes distribution is governedby a combination of higher transcendental functions, namely, Mittag-Leffler function, the furthergeneralized G-function, and the Pochhammer polynomial. In particular, this shows the existence ofan eigenproperty; that is, the system describing fractional polymer chain degradation containsreplicated and partially replicated fractional poles, whose effects are given by these functions