Introduction

Fractional-order (FO) calculus has developed for more than 300 years, but it has not attracted much attention until recent decades. Compared with the classical integer-order derivative, it is known that the fractional derivative has better performance in simulating long-memory processes and materials, abnormal diffusion, long-range interactions, long-term behaviors, power laws, allometric scaling laws, and so on. Up to now, fractional calculus has become a hot research topic due to its ability to describe fractal geometry, power law phenomena, memory characteristics, and other related processes. Fractional calculus theory and methods are widely employed in fields such as physics, viscoelastic theory, control science, diffusion phenomenon, biology, neural networks, engineering and technology as well as scientific computing.