Eur. Phys. J. Plus (2019) 134: 181
https://doi.org/10.1140/epjp/i2019-12561-x

Regular Article

New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator

¹ Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey
² Institute of Space Sciences, P.O. Box, MG-23, R 76900, Magurele, Bucharest, Romania
³ Department of Electrical and Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran
⁴ Department of Electrical Engineering, University of Bojnord, P.O. Box, 94531-1339, Bojnord, Iran
⁵ Palestine Technical University, College of Arts and Sciences, Department of Physics, P.O. Box 7, Tulkarm, Palestine

^* e-mail: a.jajarmi@ub.ac.ir

Received: 18 December 2018
Accepted: 6 February 2019
Published online: 30 April 2019

Abstract

Free motion of a fractional capacitor microphone is investigated in this paper. First, a capacitor microphone is introduced and the Euler-Lagrange equations are established. Due to the fractional derivative's the history independence, the fractional order displacement and electrical charge are used in the equations. Fractional differential equations involve in the right- and left-hand-sided derivatives which is reduced to a boundary value problem. Finally, numerical simulations are obtained and dynamical behaviors are numerically discussed.