Exactly explicit solutions of (2+1)-dimensional conformable fractional diffusive Predator–Prey model via neural networks method
4 affiliations
- 1College of Computer Science, Chengdu University
- 2Department of Mathematics, University of the Punjab
- 3Department of Computer Engineering, Biruni University
- 4Mathematics Research Center, Near East University
Abstract
In this paper, a solver is developed to obtain accurate analytical solutions for fractional partial differential equations based on artificial neural networks. By leveraging the powerful function approximation capability of neural networks in combination with the trial function method, a general analytical solution approach for fractional partial differential equations is proposed. The method is applied to a (2 + 1)-dimensional conformable fractional diffusive predator–prey system, and a series of exact analytical solutions are successfully derived. With the aid of Python mathematical software, three-dimensional surface plots, two-dimensional curve plots, gradient field plots, and contour plots in polar coordinates for selected solutions are generated to visually illustrate the morphological characteristics of the solutions. These implementations collectively verify the effectiveness and practicality of the proposed method.
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BibTeX
@article{li2026exactly,
title = {{Exactly explicit solutions of (2+1)-dimensional conformable fractional diffusive Predator–Prey model via neural networks method}},
author = {Zhao Li and Minglang Wu and Ejaz Hussain and Yakup Yildirim},
journal = {Frontiers in Physics},
year = {2026},
month = may,
doi = {10.3389/fphy.2026.1824530},
url = {https://doi.org/10.3389/fphy.2026.1824530},
note = {CC BY},
}
RIS
TY - JOUR
TI - Exactly explicit solutions of (2+1)-dimensional conformable fractional diffusive Predator–Prey model via neural networks method
AU - Zhao Li
AU - Minglang Wu
AU - Ejaz Hussain
AU - Yakup Yildirim
PY - 2026
DA - 2026/05/26
JO - Frontiers in Physics
DO - 10.3389/fphy.2026.1824530
UR - https://doi.org/10.3389/fphy.2026.1824530
AB - In this paper, a solver is developed to obtain accurate analytical solutions for fractional partial differential equations based on artificial neural networks. By leveraging the powerful function approximation capability of neural networks in combination with the trial function method, a general analytical solution approach for fractional partial differential equations is proposed. The method is applied to a (2 + 1)-dimensional conformable fractional diffusive predator–prey system, and a series of exact analytical solutions are successfully derived. With the aid of Python mathematical software, three-dimensional surface plots, two-dimensional curve plots, gradient field plots, and contour plots in polar coordinates for selected solutions are generated to visually illustrate the morphological characteristics of the solutions. These implementations collectively verify the effectiveness and practicality of the proposed method.
SN - 2296-424X
ER -