Related papers: Fractional Derivative Approach to the Self-gravita…
A comprehensive account of a new structured algorithm for obtaining nonrelativistic diffeomorphism invariances in both space and spacetime by gauging the Galilean symmetry in a generic nonrelativistic field theoretical model is provided.…
By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack…
We present a Finite Volume formulation for determining discontinuous distributions of magnetic fields within non-orthogonal and non-uniform meshes. The numerical approach is based on the discretization of the vector potential variant of the…
We derive and analyze a fully computable discrete scheme for fractional partial differential equations posed on the full space $\mathbb{R}^d$ . Based on a reformulation using the well-known Caffarelli-Silvestre extension, we study a…
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…
Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The method takes advantage of multilevel structure in expansions…
The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the…
We describe a new finite element method (FEM) to construct continuous equilibrium distribution functions of stellar systems. The method is a generalization of Schwarzschild's orbit superposition method from the space of discrete functions…
The aim of this paper is to bring together two approaches to non-conservative systems -- the generalized variational principle of Herglotz and the fractional calculus of variations. Namely, we consider functionals whose extrema are sought,…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
We discuss the possibility to solve Modern Numerical Relativity problems using finite element methods (FEM). Adopting a "user friendly" software for handling totally general systems of nonlinear partial differential equations, FEMLAB, we…
Distribution functions (DFs) for dynamically warm thin stellar disks residing in arbitrary axisymmetric potentials are presented which approximately reproduce pre-described surface-density and velocity-dispersion profiles. The functional…
In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue…
The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations…
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential…
The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators…
We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these…
We define the fractional powers $L^s=(-a^{ij}(x)\partial_{ij})^s$, $0 < s < 1$, of nondivergence form elliptic operators $L=-a^{ij}(x)\partial_{ij}$ in bounded domains $\Omega\subset\mathbb{R}^n$, under minimal regularity assumptions on the…
We study the process of dispersion of low-regularity solutions to the Schr\"odinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get a lower bound…
This article provides an accessible introduction to fractional derivatives, a concept that extends classical calculus by allowing derivatives of non-integer order. It explores both the fundamental definitions and some of the most relevant…