An exact solution of fractional Euler-Bernoulli equation for a beam with fixed-supported and fixed-free ends

Tomasz Blaszczyk, Jaroslaw Siedlecki and HongGuang Sun

Applied Mathematics and Computation, 2021, vol. 396, issue C

Abstract: In this paper we studied the fractional Euler-Bernoulli beam equation including a composition of the left and right fractional Caputo derivatives. We analyzed the equation with two types of boundary conditions (for the fixed-supported and fixed-free ends). The differential equation is converted into an integral one, taking into account the assumed boundary conditions. The obtained exact solutions contain a composition of the left and right Riemann-Liouville integrals. Finally, we presented three particular solutions for a constant, power and trigonometric function.

Keywords: Euler-Bernoulli beam equation; Fractional Caputo derivatives; Exact solution (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:396:y:2021:i:c:s0096300320308857

DOI: 10.1016/j.amc.2020.125932

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