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：我们研究了最近发展的一些涉及指数型阶跃函数的变阶微分算子的性质。由于此类算子的表征是在拉普拉斯域中进行的，因此需要借助精确的数值方法以推导其在时域中的相应行为。为此，我们开发了一种计算程序来求解这类新型的变阶分数阶微分方程。此外，我们通过一些数值实验展示了所提方法的有效性。