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

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  • Blaszczyk, Tomasz
  • Siedlecki, Jaroslaw
  • Sun, HongGuang

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.

Suggested Citation

  • Blaszczyk, Tomasz & Siedlecki, Jaroslaw & Sun, HongGuang, 2021. "An exact solution of fractional Euler-Bernoulli equation for a beam with fixed-supported and fixed-free ends," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    • Handle: RePEc:eee:apmaco:v:396:y:2021:i:c:s0096300320308857
    DOI: 10.1016/j.amc.2020.125932
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    References listed on IDEAS

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    1. Liu, Xiping & Jia, Mei, 2019. "Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 230-242.
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    Cited by:

    1. Didier Samayoa & Alexandro Alcántara & Helvio Mollinedo & Francisco Javier Barrera-Lao & Christopher René Torres-SanMiguel, 2023. "Fractal Continuum Mapping Applied to Timoshenko Beams," Mathematics, MDPI, vol. 11(16), pages 1-12, August.

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