Analytical and numerical solution of the fractional Euler–Bernoulli beam equation

Blaszczyk, Tomasz

doi:10.2140/jomms.2017.12.23

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Analytical and numerical solution of the fractional Euler–Bernoulli beam equation

Tomasz Blaszczyk

Vol. 12 (2017), No. 1, 23–34

DOI: 10.2140/jomms.2017.12.23

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

Vol. 12, No. 1, 2017

Tomasz Blaszczyk

Abstract

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