Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics
Author
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-05-08
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
We depart from the well-known one-dimensional Fisher’s equation from population dynamics and consider an extension of this model using Riesz fractional derivatives in space.
Positive and bounded initial-boundary data are imposed on a closed and bounded domain, and a fully discrete form of this fractional initial-boundary-value problem is provided next using fractional centered differences.
The fully discrete population model is implicit and linear, so a convenient vector representation is readily derived.
Under suitable conditions, the matrix representing the implicit problem is an inverse-positive matrix.
Using this fact, we establish that the discrete population model is capable of preserving the positivity and the boundedness of the discrete initial-boundary conditions.
Moreover, the computational solubility of the discrete model is tackled in the closing remarks.
American Psychological Association (APA)
Macias-Diaz, Jorge E.. 2017. Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics. Discrete Dynamics in Nature and Society،Vol. 2017, no. 2017, pp.1-7.
https://search.emarefa.net/detail/BIM-1151580
Modern Language Association (MLA)
Macias-Diaz, Jorge E.. Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics. Discrete Dynamics in Nature and Society No. 2017 (2017), pp.1-7.
https://search.emarefa.net/detail/BIM-1151580
American Medical Association (AMA)
Macias-Diaz, Jorge E.. Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics. Discrete Dynamics in Nature and Society. 2017. Vol. 2017, no. 2017, pp.1-7.
https://search.emarefa.net/detail/BIM-1151580
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1151580