Fractional precursors in random media

Fractional Precursors in Random Media

When a broadband pulse penetrates into a dissipative and dispersive medium, phase dispersion and frequency-dependent attenuation alter the pulse in a way that results in the appearance of a precursor field with an algebraic decay. We derive here the existence of precursors in nondispersive, non-dissipative, but randomly heterogeneous and multiscale media. The shape of the precursor and its frac...

Effective fractional acoustic wave equations in random multiscale media

Wave propagation in a one-dimensional random medium with shortor long-range correlations is analyzed. Multiple scattering is studied in the regime where the fluctuations of the medium parameters are small and the propagation distance is large. In this regime pulse propagation is characterized by a random time shift described in terms of a standard or fractional Brownian motion and a determinist...

Random fractional functional differential equations

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Optical precursors in transparent media

random fractional functional differential equations

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.