THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.
THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.
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DOI：
10.21608/ejmaa.2013.283529
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发表时间：
2013-01
期刊：
影响因子：
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通讯作者：
H. Jiang;F. Liu;M. Meerschaert;R. McGough
中科院分区：
文献类型：
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作者：
H. Jiang;F. Liu;M. Meerschaert;R. McGough
在时间上具有多个分数阶导数项的分数阶偏微分方程，如Szabo波动方程或幂律波动方程，描述了重要的物理现象。然而，对这些多项时空或时间分数波动方程的研究仍处于发展阶段。研究有限域上的修正幂律多项波动方程。在Caputo意义下定义多项时间分数阶导数，其阶分别属于区间(1,2],[2,3],[2,4]或（0,n） （n > 2）。导出了多项修正幂律波动方程的解析解。这些新技术是基于卢奇科定理、拉普拉斯算子的谱表示、分离变量的方法和分数阶导数技术。然后将这些一般方法应用于Szabo波动方程和幂律波动方程的特殊情况。这些方法和技术也可以推广到其他类型的多项时-空分数阶模型，包括分数阶拉普拉斯模型。
Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.