用动力系统方法研究一类时间分数阶扩散方程的精确解

Exact Solutions of a Class of Time-Fractional Diffusion Equation by Dynamic System Method

随着时代的发展,分数阶微分模型的应用越来越广泛,故对其研究非常有必要。本文在Riemann-Liouville分数阶导数的定义下利用半固定式变量分离法与动力系统理论相结合的方法,研究了一类时间分数阶扩散方程的精确解,获得了方程的一系列精确解,通过解的坐标演化图直观地展示了在不同参数条件下的扩散现象。

With the development of the times, the application of fractional differential model is more and more extensive, so it is very necessary to study it. In this paper, under the definition of Riemann-Liouville fractional derivative, the exact solution of a class of time fractional diffusion equations is studied by combining semi-fixed variable separation method with dynamic system theory, and a series of exact solutions of the equations are obtained. The diffusion phenomenon under different parameter con-ditions is intuitively displayed through the coordinate evolution diagram of the solutions.