<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper is devoted to the study of a nonlinear Euler-Bernoulli Beam type equation involving both left and right Caputo fractional derivatives. Differently from the approaches of the other papers where they established the existence of solution for the linear Euler-Bernoulli Beam type equation numerically, we use the lower and upper solutions method with some new results on the monotonicity of the right Caputo derivative. Furthermore, we give the explicit expression of the upper and lower solutions. A numerical example is given to illustrate the obtained results.</p></abstract>

This paper is devoted to the study of a nonlinear Euler-Bernoulli Beam type equation involving both left and right Caputo fractional derivatives. Differently from the approaches of the other papers where they established the existence of solution for the linear Euler-Bernoulli Beam type equation numerically, we use the lower and upper solutions method with some new results on the monotonicity of the right Caputo derivative. Furthermore, we give the explicit expression of the upper and lower solutions. A numerical example is given to illustrate the obtained results.

On generalized nonlinear Euler-Bernoulli Beam type equations

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On generalized nonlinear Euler-Bernoulli Beam type equations"}

This paper is devoted to the study of a nonlinear Euler-Bernoulli Beam type equation involving both left and right Caputo fractional derivatives. Differently...

On generalized nonlinear Euler-Bernoulli Beam type equations

Published Online: Sep 10, 2018

Page range: 90 - 100

Received: May 08, 2017

DOI: https://doi.org/10.2478/ausm-2018-0008

Keywords
Euler-Bernouli Beam equation, upper and lower solutions method, existence of solution

© 2018 Rabah Khaldi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On generalized nonlinear Euler-Bernoulli Beam type equations

Published Online: Sep 10, 2018

Page range: 90 - 100

Received: May 08, 2017

DOI: https://doi.org/10.2478/ausm-2018-0008

KeywordsEuler-Bernouli Beam equation, upper and lower solutions method, existence of solution

© 2018 Rabah Khaldi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Euler-Bernouli Beam equation, upper and lower solutions method, existence of solution