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

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 polymer chain degradation, is solved explicitly. We prove that, whether the breakup rate depends on the size of the chain breaking up or not, the evolution of the polymer sizes distribution is governed by a combina...

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Main Authors: Emile Franc Doungmo Goufo, Stella Mugisha
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2014/392792
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spelling doaj-04e1b3ddbe944e338c769bdd5224a4b62020-11-24T21:00:28ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472014-01-01201410.1155/2014/392792392792Mathematical Solvability of a Caputo Fractional Polymer Degradation Model Using Further Generalized FunctionsEmile Franc Doungmo Goufo0Stella Mugisha1Department of Mathematical Sciences, University of South Africa, Florida Science Campus, Florida, Gauteng 0003, South AfricaDepartment of Mathematical Sciences, University of South Africa, Florida Science Campus, Florida, Gauteng 0003, South AfricaThe continuous fission equation with derivative of fractional order α, describing the polymer chain degradation, is solved explicitly. We prove that, whether the breakup rate depends on the size of the chain breaking up or not, the evolution of the polymer sizes distribution is governed by a combination of higher transcendental functions, namely, Mittag-Leffler function, the further generalized G-function, and the Pochhammer polynomial. In particular, this shows the existence of an eigenproperty; that is, the system describing fractional polymer chain degradation contains replicated and partially replicated fractional poles, whose effects are given by these functions.http://dx.doi.org/10.1155/2014/392792
collection DOAJ
language English
format Article
sources DOAJ
author Emile Franc Doungmo Goufo
Stella Mugisha
spellingShingle Emile Franc Doungmo Goufo
Stella Mugisha
Mathematical Solvability of a Caputo Fractional Polymer Degradation Model Using Further Generalized Functions
Mathematical Problems in Engineering
author_facet Emile Franc Doungmo Goufo
Stella Mugisha
author_sort Emile Franc Doungmo Goufo
title Mathematical Solvability of a Caputo Fractional Polymer Degradation Model Using Further Generalized Functions
title_short Mathematical Solvability of a Caputo Fractional Polymer Degradation Model Using Further Generalized Functions
title_full Mathematical Solvability of a Caputo Fractional Polymer Degradation Model Using Further Generalized Functions
title_fullStr Mathematical Solvability of a Caputo Fractional Polymer Degradation Model Using Further Generalized Functions
title_full_unstemmed Mathematical Solvability of a Caputo Fractional Polymer Degradation Model Using Further Generalized Functions
title_sort mathematical solvability of a caputo fractional polymer degradation model using further generalized functions
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2014-01-01
description The continuous fission equation with derivative of fractional order α, describing the polymer chain degradation, is solved explicitly. We prove that, whether the breakup rate depends on the size of the chain breaking up or not, the evolution of the polymer sizes distribution is governed by a combination of higher transcendental functions, namely, Mittag-Leffler function, the further generalized G-function, and the Pochhammer polynomial. In particular, this shows the existence of an eigenproperty; that is, the system describing fractional polymer chain degradation contains replicated and partially replicated fractional poles, whose effects are given by these functions.
url http://dx.doi.org/10.1155/2014/392792
work_keys_str_mv AT emilefrancdoungmogoufo mathematicalsolvabilityofacaputofractionalpolymerdegradationmodelusingfurthergeneralizedfunctions
AT stellamugisha mathematicalsolvabilityofacaputofractionalpolymerdegradationmodelusingfurthergeneralizedfunctions
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