in this paper, we present recent results in integral inequality theory. our results are based on thefractional integration in the sense of riemann-liouville

Given a compact topological surface V with negative Euler characteristic, the Teichmüller space Teich(V ) describes the marked Riemann metrics (with constant curvature κ = −1) which it supports. More precisely, Teich(V ) is the set of equivalence classes (Vg, φ), where Vg is a hyperbolic surface with Riemann metric g and φ : V → Vg is a homeomorphism, with (Vg1 , φ1) equivalent to (Vg2 , φ2) if...

The goal of this paper is to make mathematically precise, then illustrate, how to “email” a Riemann surface. We assume each of our Riemann surfaces are orientable and connected. We will follow the notation from [2] and will cite theorems from this source whenever possible. To email a Riemann surface we want a unique Riemann surface to correspond to a set L of finitely many matrices whose entrie...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...

The focus of this research is to use a new extended beta function and develop the extensions Gauss hypergeometric functions confluent formulas that are presumed be new. Four theorems have also been defined under generalized fractional integral operators provide an image formula for extension functions. Moreover, discussed analogous statements in terms Weyl, Riemann–Liouville, Erdélyi–Kober, Sai...

A class of multidimensional integrable hierarchies connected with commutation of general (unreduced) (N+1)-dimensional vector fields containing derivative over spectral variable is considered. They are represented in the form of generating equation, as well as in the Lax-Sato form. A dressing scheme based on nonlinear vector Riemann problem is presented for this class. The hierarchies connected...

As a basic model, the fourth-order quasilinear thin film equation (the TFE– 4) with a concentration-dependent doubly degenerate mobility coefficient vanishing at two equilibrium levels u = ±1, ut = −(|1− u|uxxx)x , is studied. The basic Riemann problem for the TFE–4 with discontinuous initial data

We deal with initial-boundary value problems for systems of conservation laws in one space dimension and we focus on the so-called boundary Riemann problem. It is known that, in general, different viscous approximations provide different limits. We establish sufficient conditions to conclude that two different approximations lead to the same limit. As an application of this result, we show that...

Geodesic vector fields and other distinguished on a Riemann manifold were used in the study of free motions such manifold, we applied geometric Hamilton–Jacobi theory for search geodesic from same closed fields. These properties appropriately extended to framework Newtonian generalised systems, particular systems defined by Lagrangians mechanical type velocity-dependent forces. Conserved quanti...