Introduction to Anisotropic Nonlocal

Among them, the anisotropic nonlocal structure tensor (ANLST) has received much attention, recently.

This paper focus on the critical wave speed and the traveling wave fronts for a general anisotropic nonlocal dispersal equation with delayed nonlocal response.

Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation.

To comply with this description, the micromorphic stress-based localizing gradient damage model incorporates evolving anisotropic nonlocal interactions throughout the loading process through an anisotropic interaction tensor and a damage dependent interaction function.

Finally, we consider an anisotropic single-particle equation with nonlocal operator L is defined by the improper integrals with kernels Jj(xj) and it is a generation of an anisotropic nonlocal operator −∑j=1N(−∂xjxj)αj.

In this paper, a localizing gradient damage model with smoothed stress based anisotropic nonlocal interactions is proposed, which overcomes the limitations of conventional damage models for the accurate prediction of localized failure of quasi-brittle materials.

This paper obtains the numerical solutions of the elliptic solitons in a (1+2)-dimensional anisotropic nonlocal nonlinear fractional Schrödinger equation, and verifies their stabilities by the direct propagation method.