Numerical schemes for initialized constant and variable fractional-order derivatives: matrix approach and its analog verification. (May 2016)

• Record Type: Journal Article
• Authors: Sierociuk, Dominik; Malesza, Wiktor; Macias, Michal
• Other Names: Ionescu Clara guest-editor.; Zhou Yong guest-editor.; Machado J. A. Tenreiro guest-editor.
• Is Part Of: Journal of vibration and control. Volume 22:Number 8(2016)
• Page Start: 2032
• Page End: 2044
• Publication Date: 2016-05
• Subjects: Fractional calculus -- initial conditions -- variable-order systems -- analog model validation -- fractional differential equations; Vibration -- Periodicals; Damping (Mechanics) -- Periodicals; 620.3
• DOI: 10.1177/1077546314565438
• Languages: English
• ISSNs: 1077-5463

Abstract

This paper presents a method for including initial conditions in recursive constant and variable fractional-order derivatives. The initial conditions are assumed to be in the form of a time-constant function. The numerical scheme for solving fractional-order differential equations, given in the matrix form, is presented as well. Results obtained with the proposed numerical algorithm are compared with the analog realization of a fractional-order inertial system. For the constant-order case, analog models were built based on domino ladder approximations for 0.5 and 0.25 orders. For the variable-order case, the analog model was built based on the reductive-switching structure. Comparison with the physical systems shows the ability of the proposed method to describe the behavior of real fractional-order systems with initial conditions.