In this article, we provide constraints for the sum by employing a generalized modified form of fractional integrals Riemann-type via convex functions. The mean inequalities functions with absolute value derivatives are discovered. Hermite–Hadamard-type symmetric function explored. These results achieved using fresh and innovative methodology integrals. Some applications explored in paper brief...

We consider the semidiscrete upwind scheme (0.1) u(t, x)t + 1 ( f ( u(t, x) ) − f ( u(t, x− ) )) = 0. We prove that if the initial data ū of (0.1) has small total variation, then the solution u (t) has uniformly bounded BV norm, independent of t, . Moreover by studying the equation for a perturbation of (0.1) we prove the Lipschitz continuous dependence of u (t) on the initial data. Using a tec...

In a previous paper (Transp. Porous Media, 55(1): 47–70), algorithms are given for computing the analytical solution to the three-phase Riemann problem. Application of those algorithms requires that the wave configuration is known. The purpose of this note is to provide a procedure to determine the wave structure for any initial and injected saturation states.

We work with the system of equations describing non-stationary compressible turbulent multicomponent flow in gravitational field. assume mixture perfect inert gases. The over rough terrain is simulated use finite volume method. modified Riemann problem solved at boundary faces. roughness surface using alteration specific dissipation wall, and wall functions. Velocity profile compared experiment...

We consider the Riemann problem for non-genuinely nonlinear conservation laws where the flux function admits two inflection points. This is a simplification of van der Waals fluid pressure, which can be seen as a function of the specific volume for a specific entropy at which the system lacks the non-genuine nonlinearity. Corresponding to each inflection point, A nonclassical Riemann solver can...

Abstract. In this paper, we investigate a traffic model similar to the Lighthill–Whitham– Richards model, consisting of a hyperbolic conservation law with a discontinuous, non-convex, piecewise-linear flux. Using Dias and Figueira’s mollification framework, analytical solutions to the corresponding Riemann problem are derived. For certain initial data, these Riemann problems can generate zero w...

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

In this article, we obtain generalizations for Grüss type integral inequality by using h(x)-Riemann-Liouville fractional integral.