The integral fractional Laplacian of order $s \in (0,1)$ is a nonlocal operator. It known that solutions to the Dirichlet problem involving such an operator exhibit algebraic boundary singularity regardless domain regularity. This, in turn, deteriorates global regularity and as result convergence rate numerical solutions. For finite element discretizations, we derive local error estimates $H^s$...

An exact form of the local Whittle likelihood is studied with the intent of developing a general-purpose estimation procedure for the memory parameter (d) that does not rely on tapering or differencing prefilters. The resulting exact local Whittle estimator is shown to be consistent and to have the same N(0, 1 4 ) limit distribution for all values of d if the optimization covers an interval of ...

holds, then f is called a generalized convex function on I []. In α = , we have convex function, convexity is defined only in geometrical terms as being the property of a function whose graph bears tangents only under it []. The convexity of functions plays a significant role in many fields, for example, in biological system, economy, optimization, and so on [–]. In recent years, the fract...

The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order o(ḡ) in the coupling constant ḡ. As a first application, based on the RiemannLiouville fractional derivative definition, the fractional Zeeman effect is used to reproduce the baryon spectrum accurately. The transformation properties of the non relativistic fractiona...