Some Applications of Fractional Calculus in Engineering

Abstract

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.

Numerical approximations of fractional derivatives with applications

“…Due to the growing number of applications of fractional calculus in science and engineering (see, e.g. , ), numerical methods are being developed to provide tools for solving such problems. Using the Grünwald–Letnikov approach, it is convenient to approximate the fractional differentiation operator, D α , by generalized finite differences.…”

A numerical integration approach for fractional‐order viscoelastic analysis of hereditary‐aging structures

“…In this section, we briefly recall the main ideas of fractional calculus, when the order of integration/differentiation is allowed to vary over time. Fractional operators with variable order can be successfully used to describe several physical phenomena, as discussed in References , and among these we have the aging phenomenon, as discussed in Reference .…”

Use of the fractional order PD controller in electro-hydraulic drive

“…The paper [9] includes studies of: tuning of PID controllers using fractional calculus concepts, heat diffusion, and circuit synthesis using evolutionary algorithms, fractional control of a hexapod robot, and fractional dynamics in the trajectory control of redundant manipulators.…”