Fractional dynamics of one-dimensional linear chain

Authors

  • Bhazel H. Rara National Institute of Physics, University of the Philippines Diliman
  • Jose Perico H. Esguerra National Institute of Physics, University of the Philippines Diliman

Abstract

We consider a finite one-dimensional linear chain of N identical masses connected by Hookean springs. A classical treatment for this system is considered before the second order time derivative of the equations of motions is changed into Caputo time fractional derivative of arbitrary order α, where 1 < α < 2. Laplace transformation was used to get a solution for the motion of particles in terms of the generalized Mittag-Leffler function. Diffusion equation is also considered for the same system, using a Caputo fractional derivative of order 0 < α < 1. Laplace transformation is also used and the solution is also expressed in the Mittag-Leffler function.

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Issue

Article ID

SPP-2003-3B-02

Section

Theoretical Physics

Published

2003-10-22

How to Cite

[1]
BH Rara and JPH Esguerra, Fractional dynamics of one-dimensional linear chain, Proceedings of the Samahang Pisika ng Pilipinas 21, SPP-2003-3B-02 (2003). URL: https://proceedings.spp-online.org/article/view/SPP-2003-3B-02.