Abstract The fractional structures of variables using Riemann–Liouville notion have been analyzed by various authors. novel idea this article is to introduce the new weighted behavior on random integral inequalities. In view these, we obtain some generalized inequalities integration continuous variables.

In this paper, we give Hermite–Hadamard type inequalities of the Jensen–Mercer for Riemann–Liouville fractional integrals. We prove integral identities, and with help these identities some other eminent inequalities, such as Jensen, Hölder, power mean obtain bounds difference newly obtained inequalities.

Some new weakly singular integral inequalities are established by a method, which generalize some results of this type in previous papers. By these inequalities, we present the attractivity solutions for Riemann–Liouville fractional differential equations. Finally, several examples given to illustrate our main results.

We establish new Liouville-type theorems for the two-dimensional stationary magneto-hydrodynamic incompressible system assuming that velocity and magnetic field have bounded Dirichlet integral. The key tool in our proof is observing stream function associated to satisfies a simple drift-diffusion equation which maximum principle available.

We develop a level set method for the computation of multi-valued physical observables (density, velocity, energy, etc.) for the high frequency limit of symmetric hyperbolic systems in any number of space dimensions. We take two approaches to derive the method. The first one starts with a decoupled system of an eikonal eikonal for phase S and a transport equations for density ρ: ∂t S+H(x,∇S) = ...

I. Abstract Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over nonco...

We calculate the three-point functions in the sine-Liouville theory explicitly. The same calculation was done in the (unpublished) work of Fateev, Zamolodchikov and Zamolodchikov to check the conjectured duality between the sine-Liouville and the SL(2,R)/U(1) coset CFTs. The evaluation of correlators boils down to that of a free-field theory with a certain number of insertion of screening opera...

There are many research available on the study of a real-valued fractal interpolation function and dimension its graph. In this paper, our main focus is to dimensional results for vector-valued Riemann–Liouville fractional integral. Here, we give some which ensure that functions quite different from functions. We determine interesting bounds Hausdorff graph function. also obtain associated inva...

We investigate a nonlinear, nonlocal, and fully coupled boundary value problem containing mixed (k,ψ^)-Hilfer fractional derivative (k,ψ^)-Riemann–Liouville integral operators. Existence uniqueness results for the given are proved with aid of standard fixed point theorems. Examples illustrating main presented. The paper concludes some interesting findings.

In this article, we investigate partial integrals and derivatives of bivariate fractal interpolation functions. We prove also that the mixed Riemann-Liouville fractional integral derivative order $\gamma = (p, q); p > 0,q 0$, functions are again corresponding to some iterated function system (IFS). Furthermore, discuss transforms