TY - Jour A2 - Dzielinski，Andrzej Au - Das，Shantanu Py - 2010 DA - 2010/05/27 TI - 通过获取模态反应系列SP - 739675 VL - 2010 AB - 许多数学建模的特殊微分方程工程和物理问题导致非线性，延迟和分数级的非凡微分方程。需要一种有效的方法来分析提供符合物理现实的解决方案的数学模型。一个分数微分方程（FDE），其中前导差分运算符是riemann-liouvelli（RL）类型需要有时难以物理地涉及的分数顺序初始状态。因此，我们必须能够在空间，时间，频率，面积，体积中解决这些非凡的系统，具有实际现实。额外的常规差分方程系统及其解决方案，具有物理原理，作用 - 反应和等效的数学分解方法，作为物理学家和工程师的辅助工程师，以便于轻松地解决过程动态。该反应链从Zeroth模式反应生成到第一模式第二模式和无限模式的内部模式;平行时间或空间尺度瞬间;所有这些模式的总和都提供了整个系统反应。该模态反应如物理理论解释的完全符合Adomian分解方法（ADM）的原理。 Fractional Differential Equation (FDE) with Riemann-Liouvelli formulation linear and non-linear is solved as per ADM. In this formulation of FDE by RL method it is found that there is no need to worry about the fractional initial states; instead one can use integer order initial states (the conventional ones) to arrive at solution of FDE. This new finding too is highlighted in this paper-along with several other problems to give physical insight to the solution of extraordinary differential equation systems. This way one gets insight to Physics of General Differential Equation Systems-and its solution-by Physical Principle and equivalent mathematical decomposition method. This facilitates ease in modeling. SN - 1687-5591 UR - https://doi.org/10.1155/2010/739675 DO - 10.1155/2010/739675 JF - Modelling and Simulation in Engineering PB - Hindawi Publishing Corporation KW - ER -