Seismic wave propagation in viscoelastic media under Atangana-Baleanu fractional dynamics: Model formulation and numerical simulations

TL;DR

This paper introduces a novel seismic wave model using Atangana-Baleanu fractional derivatives, demonstrating how fractional memory influences wave attenuation and dispersion through numerical simulations.

Contribution

It formulates a new one-dimensional viscoelastic seismic-wave model based on Atangana-Baleanu fractional calculus and provides numerical methods for simulation.

Findings

Fractional memory affects wave attenuation and dispersion.

Energy decay is non-exponential with fractional derivatives.

Numerical simulations validate the model's behavior.

Abstract

We propose a one-dimensional viscoelastic seismic-wave model driven by the Atangana-BaleanuCaputo fractional derivative with a non-singular Mittag-Leffler kernel. A finite-difference discretization in space and an Adams-Bashforth-Moulton predictor-corrector scheme in time are used to compute solutions for several fractional orders. Simulations indicate that fractional memory alters both attenuation and dispersion, leading to non-exponential energy decay compared with the classical integer-order case.