（3+1）-维时空分数阶Yu-Toda-Sasa-Fukuyama方程的新精确解

大理大学学报 ›› 2025, Vol. 10 ›› Issue (12): 6-14.

（3+1）-维时空分数阶Yu-Toda-Sasa-Fukuyama方程的新精确解

昆明工业职业技术学院人文教育学院，云南安宁　650300

出版日期:2025-12-15 发布日期:2026-01-16
作者简介:陈进华，讲师，主要从事偏微分方程的精确解研究。

New Exact Solutions to the（ 3+1）-Dimensional Space-Time Fractional Yu-Toda-Sasa-Fukuyama Equation

School of Humanities Education, Kunming Vocational and Technical College of Industry, Anning, Yunnan 650300, China

Online:2025-12-15 Published:2026-01-16

摘要/Abstract

摘要： 在一致分数阶导数意义下，将分数阶非线性偏微分方程转化为常微分方程，分别运用系数为1的一元多项式函数和二
元多项式函数嵌入有理函数，得到（3+1）-维时空分数阶Yu-Toda-Sasa-Fukuyama方程的19个新精确解，其中包括10个指数函
数、3个有理函数和6个含对数函数形式的解。

关键词: （ 3+1）-维时空分数阶Yu-Toda-Sasa-Fukuyama方程, 精确解, 一致分数阶导数, 有理函数, 多项式函数

Abstract: In the sense of the conformable fractional derivative, the fractional nonlinear partial differential equation is transformed
into an ordinary differential equation. By embedding univariate polynomial functions and bivariate polynomial functions with a coefficient of 1 into rational functions, respectively, 19 new exact solutions to the （3+1）-dimensional space-time fractional Yu-Toda-Sasa-Fukuyama equation are obtained, including 10 exponential function solutions, 3 rational function solutions, and 6 solutions involving logarithmic functions.

Key words: （3+1）-dimensional space-time fractional Yu-Toda-Sasa-Fukuyama equation, exact solution, conformable fractional
derivative, rational function, polynomial function

中图分类号:

O175.29

陈进华. （3+1）-维时空分数阶Yu-Toda-Sasa-Fukuyama方程的新精确解[J]. 大理大学学报, 2025, 10(12): 6-14.

Chen Jinhua. New Exact Solutions to the（ 3+1）-Dimensional Space-Time Fractional Yu-Toda-Sasa-Fukuyama Equation[J]. Journal of Dali University, 2025, 10(12): 6-14.