We study the sample path regularity of the solution of a stochastic wave equation in spatial dimension d = 3. The driving noise is white in time and with a spatially homogeneous covariance defined as a product of a Riesz kernel and a smooth function. We prove that at any fixed time, a.s. the sample paths in the spatial variable belong to certain fractional Sobolev spaces. In addition, for any f...

We derive sharp Adams inequalities with exact growth condition for the Riesz potential and more general Riesz-like potentials on Rn. also obtain Moser-Trudinger fractional Laplacian, homogeneous elliptic differential operators constant coefficients.

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

The purpose of this note is to announce a number of results concerning the various approaches to fractional integration on the real line E as due to H. Weyl [9], M. Riesz [7], W. Feller [4] and G. O. Okikiolu [ô]. Our principal contributions are on extensions of theorems of J. L. B. Cooper [3], on the interchange of the operations of fractional integration (differentiation) and the Hilbert tran...

In this paper, we consider numerical solutions for Riesz space fractional partial differential equations with a second order time derivative. We propose Galerkin finite element scheme both the temporal and spatial discretizations. For proposed scheme, derive sharp stability estimates as well optimal priori error estimates. Extensive experiments are conducted to verify promising features of newl...

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, phys...

The fractional derivatives in the sense of modified Riemann-Liouville derivative and the improved fractional sub-equation method are employed for constructing the exact solutions of nonlinear fractional partial differential equations. By means of this method, the space-time fractional generalized Hirota-Satsuma coupled Kortewegde Vries equations are successfully solved. As a result, three types...

In this paper we consider the so called a vector metric space, which is a generalization of metric space, where the metric is Riesz space valued. We prove some common fixed point theorems for three mappings in this space. Obtained results extend and generalize well-known comparable results in the literature.