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 Delta-Dirac property have been utilized in this process. The aim of study was introduce into damped model nonlocalities associated these mentioned see effect each one them when computing Bode diagram obtained from Laplace Sumudu transform. For case, we applied both transform a solution complex space. phase for values fractional orders. We presented detailed analysis uniqueness an exact numerical approximation solution.