This paper examines the global (in time) regularity of classical solutions to the two-dimensional (2D) incompressible magnetohydrodynamics (MHD) equations with only magnetic diffusion. Here the magnetic diffusion is given by the fractional Laplacian operator (−Δ)β . We establish the global regularity for the case when β > 1. This result significantly improves previous work which requires β > 3 ...

We prove a weak maximum principle for nonlocal symmetric stable operators including the fractional Laplacian. The main focus of this work is on minimal regularity assumptions functions under consideration.

We employing a minimization arguments on appropriate Nehari manifolds, we obtain ground state solutionsfor non-local elliptic system driven by the fractional a(.)-Laplacian operator, with Dirichlet boundaryconditions type.

 This paper presents the tunable technique of the analog filter at high frequency fp = 1 MHz by used the Fractional-order   n   step, where n is an original of integerorder on circuit and  is an approximation order step 0 1    , An approximation order is designed from the Fractance circuits, and also presents the approximation function of the Fractional-order Laplacian s  design on th...

Abstract. We introduce and analyze a spectral vanishing viscosity approximation of periodic fractional conservation laws. The fractional part of these equations can be a fractional Laplacian or other non-local operators that are generators of pure jump Lévy processes. To accommodate for shock solutions, we first extend to the periodic setting the Kružkov-Alibaud entropy formulation and prove we...

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is computationally demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code al...

The Laplacian raised to fractional powers can be used to generate scale spaces as was shown in recent literature. This was later extended for inhomogeneous diffusion processes and more general functions of the Laplacian and studied for the Perona-Malik case. In this paper we extend the results to the truly anisotropic Beltrami flow. We additionally introduce a technique for splitting up the wor...