Quantum mechanics

Voltage

Algebraic number

Pure mathematics

Lagrangian

Applied mathematics

Euler's formula

Capacitor

Algebraic equation

Physics

Nonlinear system

Kernel (algebra)

Mathematics

Mathematical analysis

Fractional calculus

Results in Physics

In this study, a new and general fractional formulation is presented to investigate the complex behaviors of a capacitor microphone dynamical system. Initially, for both displacement and electrical charge, the classical Euler–Lagrange equations are constructed by using the classical Lagrangian approach. Expanding this classical scheme in a general fractional framework provides the new fractional Euler–Lagrange equations in which non-integer order derivatives involve a general function as their kernel. Applying an appropriate matrix approximation technique changes the latter fractional formulation into a nonlinear algebraic system. Finally, the derived system is solved numerically with a discussion on its dynamical behaviors. According to the obtained results, various features of the capacitor microphone under study are discovered due to the flexibility in choosing the kernel, unlike the previous mathematical formalism.

A new and general fractional Lagrangian approach: A capacitor microphone case study