分数阶广义扰动热波方程

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 452-459.

分数阶广义扰动热波方程

欧阳成^1,*(),汪维刚²,莫嘉琪³

¹ 湖州师范学院理学院浙江湖州 313000
² 合肥幼儿师范高等专科学校合肥 230011
³ 安徽师范大学数学与统计学院安徽芜湖 241003

收稿日期:2017-09-20 出版日期:2020-04-26 发布日期:2020-05-21
通讯作者: 欧阳成 E-mail:oyc@zjhu.edu.cn
基金资助:
国家自然科学基金(11771005);浙江省自然科学基金(LY16A010011);安徽省教育厅自然科学重点基金(KJ2018A0964);安徽省教育厅自然科学重点基金(KJ2019A1261)

The Fractional Generalized Disturbed Thermal Wave Equation

Cheng Ouyang^1,*(),Weigang Wang²,Jiaqi Mo³

¹ Faculty of Science, Huzhou University, Zhejiang Huzhou 313000
² Department of Basic, Hefei Preschool Education College, Hefei 230011
³ School of Mathematics & Statistics, Anhui Normal University, Anhui Wuhu 241003

Received:2017-09-20 Online:2020-04-26 Published:2020-05-21
Contact: Cheng Ouyang E-mail:oyc@zjhu.edu.cn
Supported by:
the NSFC(11771005);the NSF of Zhejiang Province(LY16A010011);the NSF of the Education Department of Anhui Province(KJ2018A0964);the NSF of the Education Department of Anhui Province(KJ2019A1261)

摘要/Abstract

摘要：

研究了一类分数阶广义非线性扰动热波方程.首先用奇异慑动方法，求出了分数阶广义非线性扰动热波方程初始边值问题的任意次近似解析解.然后利用泛函分析不动点定理证明了它的一致有效性，最后简述了它的物理意义.求得的近似解析解，弥补了单纯用数值方法求模拟解的不足.

关键词: 热波, 分数阶, 奇异摄动

Abstract:

A class of generalized fractional nonlinear disturbed thermal wave equation is considered. Firstly, the arbitrary order approximate analytic solutions for the fractional generalized nonlinear disturbed thermal wave equation initial boundary value problem was constructed by using the singular perturbation method. And the uniformly valid asymptotic expansion was proofed by using the fixed point theory of the functional analysis. The physical sense of the solution was stated simply. The approximate analysis solution makes up not enough the simple numerical simulation solution.

Key words: Thermal wave, Fractional order, Singular perturbation

中图分类号:

O175.19

欧阳成,汪维刚,莫嘉琪. 分数阶广义扰动热波方程[J]. 数学物理学报, 2020, 40(2): 452-459.

Cheng Ouyang,Weigang Wang,Jiaqi Mo. The Fractional Generalized Disturbed Thermal Wave Equation[J]. Acta mathematica scientia,Series A, 2020, 40(2): 452-459.

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