Existence Results for a Michaud Fractional, Nonlocal, and Randomly Position Structured Fragmentation Model
Joint Authors
Mugisha, Stella
Maritz, Riëtte
Doungmo Goufo, Emile Franc
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-12
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Until now, classical models of clusters’ fission remain unable to fully explain strange phenomena like the phenomenon of shattering (Ziff and McGrady, 1987) and the sudden appearance of infinitely many particles in some systems having initial finite number of particles.
That is why there is a need to extend classical models to models with fractional derivative order and use new and various techniques to analyze them.
In this paper, we prove the existence of strongly continuous solution operators for nonlocal fragmentation models with Michaud time derivative of fractional order (Samko et al., 1993).
We focus on the case where the splitting rate is dependent on size and position and where new particles generating from fragmentation are distributed in space randomly according to some probability density.
In the analysis, we make use of the substochastic semigroup theory, the subordination principle for differential equations of fractional order (Prüss, 1993, Bazhlekova, 2000), the analogy of Hille-Yosida theorem for fractional model (Prüss, 1993), and useful properties of Mittag-Leffler relaxation function (Berberan-Santos, 2005).
We are then able to show that the solution operator to the full model is positive and contractive.
American Psychological Association (APA)
Doungmo Goufo, Emile Franc& Maritz, Riëtte& Mugisha, Stella. 2014. Existence Results for a Michaud Fractional, Nonlocal, and Randomly Position Structured Fragmentation Model. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-465867
Modern Language Association (MLA)
Doungmo Goufo, Emile Franc…[et al.]. Existence Results for a Michaud Fractional, Nonlocal, and Randomly Position Structured Fragmentation Model. Mathematical Problems in Engineering No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-465867
American Medical Association (AMA)
Doungmo Goufo, Emile Franc& Maritz, Riëtte& Mugisha, Stella. Existence Results for a Michaud Fractional, Nonlocal, and Randomly Position Structured Fragmentation Model. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-465867
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-465867