Analytical and numerical analysis of damped harmonic oscillator model with nonlocal operators

Abstract

Nonlocal operators with different kernels were used here to obtain more general harmonic oscillator models. Power law, exponential decay, and the generalized Mittag-Leffler kernels with Delta-Dirac property have been utilized in this process. The aim of this study was to introduce into the damped harmonic oscillator model nonlocalities associated with these mentioned kernels and see the effect of each one of them when computing the Bode diagram obtained from the Laplace and the Sumudu transform. For each case, we applied both the Laplace and the Sumudu transform to obtain a solution in a complex space. For each case, we obtained the Bode diagram and the phase diagram for different values of fractional orders. We presented a detailed analysis of uniqueness and an exact solution and used numerical approximation to obtain a numerical solution.

Keywords

• damped harmonic oscillator
• nonlocal operators
• bode diagram
• existence and uniqueness of the solutions
• numerical methods
• 42b37
• 34a12
• 26a33
• 65r10