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Research Article

Year : 2018 | Volume: 4 | Issue: 2 | Pages: 49-57

Analytical Solution of Linear Fractionally Damped Oscillator by Elzaki Transformed Method

Jamshaid ul Rahman1*, Muhammad Suleman, Dianchen Lu, Naveed Anjum2

DOI: 10.18831/djmaths.org/2018021005

Corresponding author

Jamshaid ul Rahman*

School of Mathematical Sciences, University of Science and Technology of China, Hefei, China.

  • 1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, China.

Received on: 2018/03/26

Revised on: 2018/05/21

Accepted on: 2018/06/13

Published on: 2018/06/20

  • Analytical Solution of Linear Fractionally Damped Oscillator by Elzaki Transformed Method, Jamshaid ul Rahman, Muhammad Suleman, Dianchen Lu, Naveed Anjum., 2018/06/20, DJ Journal of Engineering and applied Mathematics. , 4(2): 49-57, http://dx.doi.org/10.18831/djmaths.org/12018021005.

    Published on: 2018/06/20

Abstract

In this manuscript, linearly and fractionally damped oscillator equation is solved with the help of Caputo fractional derivatives. For 0a 1 oscillation equations change from undamped to damped, whereas a represents the order of Caputo derivative. Analytical solution of nine different cases of critically damped, over-damped and undamped differential equations is found by Elzaki transformation. The oscillatory frequency of three cases of differential equation rises with the increase in damping order before falling to its limiting value provided by the ordinary oscillator damped equation whereas the frequency of oscillation of remaining six cases declines with the increase in derivative order (damping order).

Keywords

Elzaki transformation, linear oscillator, fractional damping, oscillation,Riemann-Liouville derivative .