Eur. Phys. J. Special Topics 193, 93-104 (2011)
https://doi.org/10.1140/epjst/e2011-01384-4

Regular Article

A Physical experimental study of variable-order fractional integrator and differentiator

¹ Department of Electronic Engineering, Dalian University of Technology, Dalian 116024, China
² Institute of Soft Matter Mechanics, Department of Engineering Mechanics, Hohai University 210098, China
³ CSOIS, Electrical and Computer Engineering Department, Utah State University, Logan, UT 84322, USA

^a e-mail: yangQuan.chen@usu.edu

Received: 1 December 2010
Revised: 27 January 2011
Published online: 4 April 2011

Abstract

Recent research results have shown that many complex physical phenomena can be better described using variable-order fractional differential equations. To understand the physical meaning of variable-order fractional calculus, and better know the application potentials of variable-order fractional operators in physical processes, an experimental study of temperature-dependent variable-order fractional integrator and differentiator is presented in this paper. The detailed introduction of analogue realization of variable-order fractional operator, and the influence of temperature to the order of fractional operator are presented in particular. Furthermore, the potential applications of variable-order fractional operators in PI^λ(t)D^μ(t) controller and dynamic-order fractional systems are suggested.