Fractional oscillator equation: analytical solution and algorithm for its approximate computation-Reference-Cited by-同舟云学术

Fractional oscillator equation: analytical solution and algorithm for its approximate computation

Published:2015-01-20 Issue:8 Volume:22 Page:2045-2052
ISSN:1077-5463
Container-title:Journal of Vibration and Control
language:en
Short-container-title:Journal of Vibration and Control

Author:

Blaszczyk Tomasz¹,Ciesielski Mariusz²

Affiliation:

1. Czestochowa University of Technology, Institute of Mathematics, Czestochowa, Poland

2. Czestochowa University of Technology, Institute of Computer and Information Sciences, Czestochowa, Poland

Abstract

In this paper the fractional oscillator equation in a finite time interval is considered. The fractional equation with derivatives of order [Formula: see text] is transformed into its corresponding integral form, by using the symbolic calculus method, in which the binomial expansion of the inverse integral operator is used. A new fractional integral operator is introduced. A numerical algorithm to approximate the solution of the considered equation is proposed. In the final part of this paper examples of numerical solutions of this equation are given.

Publisher

SAGE Publications

Subject

Mechanical Engineering,Mechanics of Materials,Aerospace Engineering,Automotive Engineering,General Materials Science

Link

http://journals.sagepub.com/doi/pdf/10.1177/1077546314566836

Reference45 articles.

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2. Dynamics of the fractional oscillator

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4. Generalized Euler—Lagrange Equations and Transversality Conditions for FVPs in terms of the Caputo Derivative

5. Generalized variational calculus in terms of multi-parameters fractional derivatives

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