Space‐time fractional Dirichlet problems

Space-time Fractional Dirichlet Problems

This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes timechanged by an inverse stable subordinator whose index equals the order of the fractional time derivative. Some applications are given, to demonstrate how to specify a well-posed Dirichlet problem for space-time fractional diffusions...

Fractional S-branes on a Spacetime Orbifold

Unstable D-branes are central objects in string theory, and exist also in time-dependent backgrounds. In this paper we take first steps to studying brane decay in spacetime orbifolds. As a concrete model we focus on the R/Z2 orbifold. We point out that on a spacetime orbifold there exist two kinds of S-branes, fractional S-branes in addition to the usual ones. We investigate their construction ...

Heat Kernel Estimates for Dirichlet Fractional Laplacian

In this paper, we consider the fractional Laplacian −(−∆)α/2 on an open subset in R with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such Dirichlet fractional Laplacian in C open sets. This heat kernel is also the transition density of a rotationally symmetric α-stable process killed upon leaving a C open set. Our results are the first sharp two-sided ...

Positive Solutions of Nonlinear Fractional Boundary Value Problems with Dirichlet Boundary Conditions

In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of posit...

Dirichlet Problems with Asymmetric Nonlinearities