Plankton-Oxygen Dynamics in the Context of Climate Change: A Fractional Model with A Probability Density Function Approach
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914157636354048 |
|---|---|
| author | El-Borai, Mahmoud M. El-Sayed, Wagdy G. Habib, Mahmoud A. |
| author_facet | El-Borai, Mahmoud M. El-Sayed, Wagdy G. Habib, Mahmoud A. |
| contents | We analyze how climate change affects marine oxygen production by modeling plankton--oxygen dynamics with a fractional-order nonlinear system and establishing rigorous conditions for the model's well-posedness. We formulate a three-dimensional system $d^αx(t)/dt^α= A x(t) + f(x(t))$, where $A$ is a diagonal $3\times 3$ matrix and $f$ is nonlinear. We (i) rigorously state the model, (ii) derive a Lipschitz constant for $f$ under suitable assumptions, and (iii) prove existence, uniqueness, and continuous dependence on initial data using a fractional formula with a probability density kernel and a generalized Gr"onwall inequality. Under the stated conditions, $f$ satisfies a computable Lipschitz bound that yields existence and uniqueness of solutions for the fractional system, and the solutions depend continuously on initial conditions, establishing the well-posedness of the plankton--oxygen model. We introduce a fractional, PDF-kernel--based framework for plankton--oxygen dynamics and provide general proofs of well-posedness via a generalized Gr"onwall approach, capturing memory effects that classical integer-order models miss. These results justify numerical simulations and sensitivity analyses of fractional marine-ecosystem models, providing a sound basis for testing mitigation and management strategies affecting oxygen dynamics and supporting evidence-based policies for protecting marine ecosystems under global warming. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05742 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Plankton-Oxygen Dynamics in the Context of Climate Change: A Fractional Model with A Probability Density Function Approach El-Borai, Mahmoud M. El-Sayed, Wagdy G. Habib, Mahmoud A. Analysis of PDEs Dynamical Systems We analyze how climate change affects marine oxygen production by modeling plankton--oxygen dynamics with a fractional-order nonlinear system and establishing rigorous conditions for the model's well-posedness. We formulate a three-dimensional system $d^αx(t)/dt^α= A x(t) + f(x(t))$, where $A$ is a diagonal $3\times 3$ matrix and $f$ is nonlinear. We (i) rigorously state the model, (ii) derive a Lipschitz constant for $f$ under suitable assumptions, and (iii) prove existence, uniqueness, and continuous dependence on initial data using a fractional formula with a probability density kernel and a generalized Gr"onwall inequality. Under the stated conditions, $f$ satisfies a computable Lipschitz bound that yields existence and uniqueness of solutions for the fractional system, and the solutions depend continuously on initial conditions, establishing the well-posedness of the plankton--oxygen model. We introduce a fractional, PDF-kernel--based framework for plankton--oxygen dynamics and provide general proofs of well-posedness via a generalized Gr"onwall approach, capturing memory effects that classical integer-order models miss. These results justify numerical simulations and sensitivity analyses of fractional marine-ecosystem models, providing a sound basis for testing mitigation and management strategies affecting oxygen dynamics and supporting evidence-based policies for protecting marine ecosystems under global warming. |
| title | Plankton-Oxygen Dynamics in the Context of Climate Change: A Fractional Model with A Probability Density Function Approach |
| topic | Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2511.05742 |