A Computational Approach to Exponential-Type Variable-Order Fractional Differential Equations

We investigate the properties of some recently developed variable-order differential operators involving order transition functions of exponential type. Since the characterization 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 technique.

Automated summary

We investigate the properties of variable-order differential operators with order transition functions of exponential type. Accurate numerical methods are necessary to derive the corresponding behaviors in the time domain. We develop a computational procedure to solve these novel variable-order fractional differential equations, and provide numerical experiments to demonstrate the effectiveness of the proposed technique.