【摘要】 给出了求解分数阶动态系统的一个非常有效的数值方法。本方法不但公式简单易编程,而且具有计算精度高、运算速度快等优点。本方法的思想是依据在实际应用中,通常要求给定函数有足够的连续性和光滑性,这就使得它们的Riemann-Liouville和Grünwald-Letnicov分数导数完全等价。这样在分数阶动态系统中,可以利用Grünwald-Letnicov 分数导数的1阶或高阶近似表达式来近似表示Riemann-Liouville分数导数。最后给出一个仿真实例,说明所给方法的有效性。更多还原

【Abstract】 A very efficient numerical algorithm for solving fractional order dynamic systems is given. This algorithm not only has a simple formula, which is easy to program, but also has the virtue of a high precision and fast computation time. The main reason is because in actual applications it is usually needed that a given function must have enough continuities and smoothness, and that its Riemann-Liouville and Grünwald-Letnicov fractional derivatives are equivalent. This makes it possible to approximate Riemann-Liouville fractional derivatives by using the first order or higher order approximation of Grünwald-Letnicov fractional derivatives in fractional order dynamic systems. An example is given to indicate the effectiveness of the method aforementioned.更多还原