Vol. 12, No. 1, 2017

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ISSN: 1559-3959
Analytical and numerical solution of the fractional Euler–Bernoulli beam equation

Tomasz Blaszczyk

Vol. 12 (2017), No. 1, 23–34
Abstract

In this paper a new formulation of the Euler–Bernoulli beam equation is proposed, which is based on fractional calculus. The fractional Euler–Bernoulli beam equation is derived by using a variational approach. Such formulation leads to an equation containing left and right fractional Caputo derivatives simultaneously. The obtained equation is transformed into an integral equation and then is solved analytically and numerically. Finally, examples of computations and error analysis are shown.

Keywords
Euler–Bernoulli beam equation, Fractional Euler–Lagrange equation, Analytical and numerical solution, Caputo derivatives
Milestones
Received: 5 January 2016
Revised: 13 May 2016
Accepted: 27 May 2016
Published: 26 November 2016
Authors
Tomasz Blaszczyk
Institute of Mathematics
Czestochowa University of Technology
Al. Armii Krajowej 21
42-200 Czestochowa
Poland