Version 1
: Received: 5 October 2024 / Approved: 7 October 2024 / Online: 8 October 2024 (10:01:52 CEST)
How to cite:
Fazal, F.; Sulaiman, M.; Bassir, D.; Alshammari, F. S.; Laouini, G. Quantitative Analysis of the Fractional Fokker–Planck Levy Equation via a Modified Physics-Informed Neural Network Architecture. Preprints2024, 2024100525. https://doi.org/10.20944/preprints202410.0525.v1
Fazal, F.; Sulaiman, M.; Bassir, D.; Alshammari, F. S.; Laouini, G. Quantitative Analysis of the Fractional Fokker–Planck Levy Equation via a Modified Physics-Informed Neural Network Architecture. Preprints 2024, 2024100525. https://doi.org/10.20944/preprints202410.0525.v1
Fazal, F.; Sulaiman, M.; Bassir, D.; Alshammari, F. S.; Laouini, G. Quantitative Analysis of the Fractional Fokker–Planck Levy Equation via a Modified Physics-Informed Neural Network Architecture. Preprints2024, 2024100525. https://doi.org/10.20944/preprints202410.0525.v1
APA Style
Fazal, F., Sulaiman, M., Bassir, D., Alshammari, F. S., & Laouini, G. (2024). Quantitative Analysis of the Fractional Fokker–Planck Levy Equation via a Modified Physics-Informed Neural Network Architecture. Preprints. https://doi.org/10.20944/preprints202410.0525.v1
Chicago/Turabian Style
Fazal, F., Fahad Sameer Alshammari and Ghaylen Laouini. 2024 "Quantitative Analysis of the Fractional Fokker–Planck Levy Equation via a Modified Physics-Informed Neural Network Architecture" Preprints. https://doi.org/10.20944/preprints202410.0525.v1
Abstract
An innovative approach is utilized in this paper to solve the Fractional Fokker–Planck–Levy (FFPL) equation. A hybrid technique is designed by combining the finite difference method (FDM), Adams numerical technique, and physics-informed neural network (PINN) architecture, namely, the FDM-APINN, to solve the fractional Fokker‒Planck‒Levy (FFPL) equation numerically. Two scenarios of the FFPL equation are considered by varying the value of α (i.e., 1.75,1.85). Moreover, three cases of each scenario are numerically studied for different discretized domains with 100,200 and 500 points in x∈[-1,1] and t∈[0,1]. For the FFPL equation, solutions are obtained via the FDM-APINN technique via 1000,2000, and 5000 iterations. The errors, loss function graphs, and statistical tables are presented to validate our claim that the FDM-APINN is a better alternative intelligent technique for handling fractional-order partial differential equations with complex terms. FDM-APINN can be extended by using nongradient-based bioinspired computing for higher-order fractional partial differential equations.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
