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

‎We study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎These equations will be converted to a system of‎ ‎singular integral equations with Cauchy type kernels‎. ‎Using‎ ‎Chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of Cauchy type singular integral equation which will ...

The so called integrating factor method, used to find solutions of ordinary differential equations of a certain type, is well known. In this article, we extend it to equations with values in a Banach space. Besides being of interest in itself, this extension will give us the opportunity to touch on a few topics that are not usually found in the relevant literature. Our presentation includes var...

We study the Cauchy problem for the Aw-Rascle-Zhang model for traffic flow with a flux constraint at x = 0. More precisely we consider the Riemann solver, conserving the number of cars at x = 0 but not the generalized momentum, introduced in [9] for the problem with flux constrained. For such a Riemann solver, we prove existence of a solution for the Cauchy problem. The proof is based on the wa...

An algorithm is provided for the fast and accurate computation of the solution of nonhomogeneous Cauchy-Riemann equations in the complex plane in the interior of a unit disk. The algorithm is based on the representation of the solution in terms of a double integral, some recursive relations in Fourier space, and fast Fourier transforms. The numerical evaluation of the solution at N2 points on a...

Properties of the Cauchy–Riemann–Fueter equation for maps between quaternionic manifolds are studied. Spaces of solutions in case of maps from a K3–surface to the cotangent bundle of a complex projective space are computed. A relationship between harmonic spinors of a generalized nonlinear Dirac operator and solutions of the Cauchy– Riemann–Fueter equation are established.

The construction of analogues of the Cauchy kernel is crucial for the solution of Riemann–Hilbert problems on compact Riemann surfaces. A formula for the Cauchy kernel can be given as an infinite sum over the elements of a Schottky group, and this sum is often used for the explicit evaluation of the kernel. In this paper a new formula for a quasi-automorphic analogue of the Cauchy kernel in ter...

The Riemann integral is founded on the following idea: divide up the domain of a function f : [a, b] −→ R into subintervals, estimate f from above and below on each interval, and approximate the integral of f by the upper and lower sums—the summation of the widths of the intervals times the upper and lower estimates on each. The limit over partitions of [a, b] of these two approximations, shoul...

in this paper, we use the riemann-liouville fractionalintegrals to establish some new integral inequalities related tochebyshev's functional in the case of two differentiable functions.