We investigate the properties of some recently developed variable-order differential operators involving order transition functions of exponential type. Since the characterisation of such operators is performed in the Laplace domain it is necessary to resort to accurate numerical methods to derive the corresponding behaviours in the time domain. In this regard, we develop a computational procedure to solve variable-order fractional differential equations of this novel class. Furthermore, we provide some numerical experiments to show the effectiveness of the proposed techniques.
翻译:我们调查一些最近开发的可变顺序差异操作员的特性,这些可变顺序差异操作员涉及指数型命令转换功能。由于这些操作员的特性是在拉帕特域进行的,因此有必要采用精确的数字方法来得出时间域的相应行为。在这方面,我们开发了一个计算程序,以解决这一新型类的可变顺序分数等方程。此外,我们提供一些数字实验,以显示拟议技术的有效性。</s>