Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics
| Autor: | J. E. Macías-Díaz |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Discrete Dynamics in Nature and Society, Vol 2017 (2017) |
| Druh dokumentu: | article |
| ISSN: | 1026-0226 1607-887X |
| DOI: | 10.1155/2017/5716015 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|