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Numerical solution of the fractional Euler-Lagrange’s equations of a thin elastica model


In this manuscript, we investigated the fractional thin elastic system. We studied the obtained fractional Euler-Lagrange’s equations of the system numerically. The numerical study is based on Grünwald–Letnikov approach, which is power series expansion of the generating function. We present an illustrative example of the proposed numerical model of the system.

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The work of Ivo Petras was supported in part by Grants VEGA: 1/0552/14, 1/0908/15, and APVV-0482-11.

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Baleanu, D., Asad, J.H. & Petras, I. Numerical solution of the fractional Euler-Lagrange’s equations of a thin elastica model. Nonlinear Dyn 81, 97–102 (2015).

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  • Riemann–Liouville derivatives
  • Vibration
  • Thin elastica
  • Fractional Euler-Lagrange equations
  • Grünwald–Letnikov approach