In this paper, we study a non-local diffusion problem that involves three different fractional Laplacian operators acting on two domains. Each domain has an associated operator governs the it, and third serves as coupling mechanism between of them. The model proposed is gradient flow energy functional. first part provide results about existence solutions conservation mass. second encompasses [F...

Fractional variants of distance-based parameters have application in the fields sensor networking, robot navigation, and integer programming problems. Complex networks are exceptional which exhibit significant topological features become quintessential research area field computer science, biology, mathematics. Owing to possibility that many real-world systems can be intelligently modeled repre...

We consider empirical processes associated with high-frequency observations of a fractional Brownian motion (fBm) X Hurst parameter H?(0,1), and derive conditions under which these verify (possibly uniform) law large numbers, as well second order limit theorem. devote specific emphasis to the “zero energy” case, corresponding kernel whose integral on real line equals zero. Our asymptotic result...

Fractional branes on the non-compact orbifold C3/Z5 are studied. First, the boundary state description of the fractional branes are obtained. The open-string Witten index calculated using these states reproduces the adjacency matrix of the quiver of Z5. Then, using the toric crepant resolution of the orbifold C3/Z5 and invoking the local mirror principle, B-type branes wrapped on the holomorphi...

In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented an...

Using the theory of generalized random fields on fractional Sobolev spaces on bounded domains, and the concept of dual generalized random field, this paper introduces a class of random fields with fractional-order pure point spectra. The covariance factorization of an a-generalized random field having a dual is established, leading to a white-noise linearfilter representation, which reduces to ...

Texture image segmentation plays an important role in texture analysis. This paper presents an approach to image segmentation by texture classification based on fractional discrimination functions. The idea behind this method is to enhance the texture edge points b y means of image decomposition and contextual filtering in terms of the proposed fractional function. In addition, such function is...

Texture image segmentation plays an important role in texture analysis. This paper presents an approach to image segmentation by texture classification based on fractional discrimination functions. The idea behind this method is to enhance the texture edge points b y means of image decomposition and contextual filtering in terms of the proposed fractional function. In addition, such function is...

In this paper, we prove the existence and uniqueness of a nonlinear perturbed stochastic fractional integro-differential equation of Volterra-Itô type involving nonlocal initial condition by using the theory of admissibility of integral operator and Banach fixed-point principle. Also the stability and boundedness of the second moments of the stochastic solution are studied. In addition, an appl...

In the Fractional Quantum Hall state, we introduce a bi-local mean field and get vortex mean field solutions. Rotational invariance is imposed and the solution is constructed by means of numerical self-consistent method. It is shown that vortex has a fractional charge, a fractional angular momentum and a magnetic field dependent energy. In ν = 1/3 state, we get finite energy gap at B = 10, 15, ...