Open AccessSolving the Oscillation Equation With Fractional Order Damping Term Using a New Fourier Transform Method
Author(s) -
Özlem Öztürk Mızrak
Publication year - 2017
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v13i5.6483
Subject(s) - mathematics , fractional calculus , fourier transform , mathematical analysis , oscillation (cell signaling) , fractional fourier transform , order (exchange) , transformation (genetics) , term (time) , fourier series , fourier analysis , physics , biochemistry , chemistry , genetics , finance , quantum mechanics , gene , economics , biology
We propose an adapted Fourier transform method that gives the solution of an oscillation equation with a fractional damping term in ordinary domain. After we mention a transformation of cosmic time to individual time (CTIT), we explain how it can reduce the problem from fractional form to ordinary form when it is used with Fourier transformation, via an example for 1 < alpha < 2; where alpha is the order of fractional derivative. Then, we give an application of the results.