Existence and multiplicity results for the fractional Laplacian in bounded domains

Fractional Laplacian in bounded domains.

The fractional Laplacian operator -(-delta)(alpha/2) appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely, hopping ...

Existence and multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations

In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.

Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems

In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.

Existence and Multiplicity Results for the Boundary Value Problem of Nonlinear Fractional Differential Equations

In this paper, we devote to investigation of the existence of positive solutions for the boundary value problem of nonlinear fractional differential equations { D0+u(t)+ f (t,u(t)) = 0, 0 < t < 1, u(0) = u′(0) = · · ·u(n−2)(0) = D0+u(1), where D0+ , D β 0+ are the standard Riemann-Liouville fractional derivative, n− 1 < α n , n−2 β n−1 , n 3 . By means of constructing an exact cone of the Banac...

Multiplicity Results of Positive Radial Solutions for p-Laplacian Problems in Exterior Domains