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：我们研究了一些近期发展的涉及指数型阶跃函数的变阶微分算子的性质。由于此类算子的特征化是在拉普拉斯域中进行的，因此需要借助精确的数值方法在时域中推导相应的行为。为此，我们开发了一种计算程序来求解这类新型变阶分数阶微分方程。此外，我们提供了一些数值实验以展示所提技术的有效性。