一个2+1维时间分数阶热传导模型的精确解及其演化现象  

Exact Solutions and Evolution Phenomenon of a (2+1) Dimensional Time Fractional Heat-Conduction Model

作　　者：李文 芮伟国 LI Wen;RUI Weiguo(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《昆明理工大学学报（自然科学版）》2022年第6期189-196,共8页Journal of Kunming University of Science and Technology(Natural Science)

基　　金：国家自然科学基金项目(11361023);重庆市科委基础研究与前沿探索专项项目(cstc2018jcyjAX0766)。

摘　　要：通过一种半固定式的变量分离法研究了一个2+1维的时间分数阶热传导模型,并在Bessel方程的解及其相关性质的帮助下,获得了该模型的两类精确解的一般表达式.在不同的初值条件和边界条件下,给出了相应的特解形式,然后通过解的三维坐标图形直观地展示了解随空间变量演化的物理学现象,从而揭示了模型所蕴含的温度在热传导过程中的变化规律.A 2+1-dimensional time fractional heat-conduction model is studied by using a separation method of semi-fixed variable.With the help of the solutions of the Bessel equation and their relevant properties, the general expressions of two kinds of exact solutions of the model are obtained.Under different initial value conditions and boundary conditions, the forms of corresponding special solutions are given, and then the physical phenomena evolving with spatial variables are intuitively illustrated by 3 D-graphs, so as to reveal the variation law of temperature in the heat-conduction process which contains the model.

关 键 词：分数阶微分方程 热传导方程 BESSEL方程 Caputo型微分算子 分离变量法 

分 类 号：O175[理学—数学]