Solving the exactly explicit solutions of the conformable space-time fractional Phi-4 equation via neural networks method

IF 2.7 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physics Letters A Pub Date : 2026-06-15 Epub Date: 2026-02-27 DOI:10.1016/j.physleta.2026.131535

Zhao Li

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引用次数: 0

Abstract

The challenge of obtaining accurate analytical solutions for fractional partial differential equation is addressed in this study, a problem deemed important due to the critical role of fractional partial differential equation in modeling complex phenomena with memory and non-local effects. This article aims to study a solver based on artificial neural networks for obtaining accurate analytical solutions of fractional partial differential equation. A general analytical solution method for fractional partial differential equations is proposed by utilizing the powerful function approximation ability of neural networks and combining it with the trial function method. The method is applied to the fractional Phi-4 equation and a series of exact analytical solutions are obtained. In addition, with the help of Matlab mathematical software, three-dimensional graphics, two-dimensional curves, and contour maps of partial solutions are drawn to visually display the morphological characteristics of the understanding, verifying the effectiveness and practicality of the proposed method.

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利用神经网络方法求解符合时空分数阶pi -4方程的精确显式解

由于分数阶偏微分方程在模拟具有记忆和非局部效应的复杂现象中起着至关重要的作用，本研究解决了分数阶偏微分方程精确解析解的难题。本文旨在研究一种基于人工神经网络的分数阶偏微分方程精确解析解求解器。利用神经网络强大的函数逼近能力，将其与试函数法相结合，提出了分数阶偏微分方程的一般解析解方法。将该方法应用于分数阶Phi-4方程，得到了一系列精确解析解。此外，借助Matlab数学软件绘制了部分解的三维图形、二维曲线和等高线图，直观地展示了所理解的形态特征，验证了所提方法的有效性和实用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physics Letters A 物理-物理：综合

CiteScore

5.10

自引率

3.80%

发文量

493

审稿时长

30 days

期刊介绍： Physics Letters A offers an exciting publication outlet for novel and frontier physics. It encourages the submission of new research on: condensed matter physics, theoretical physics, nonlinear science, statistical physics, mathematical and computational physics, general and cross-disciplinary physics (including foundations), atomic, molecular and cluster physics, plasma and fluid physics, optical physics, biological physics and nanoscience. No articles on High Energy and Nuclear Physics are published in Physics Letters A. The journal''s high standard and wide dissemination ensures a broad readership amongst the physics community. Rapid publication times and flexible length restrictions give Physics Letters A the edge over other journals in the field.