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.

Discrete maps with long-term memory are obtained from nonlinear differential equations with Riemann–Liouville and Caputo fractional derivatives. These maps are generalizations of the well-known universal map. The memory means that their present state is determined by all past states with special forms of weights. To obtain discrete maps from fractional differential equations, we use the equival...

Using the Deift-Zhou steepest descent method, we derive locally uniform asymptotic formulas for the Meixner polynomials. So far as we know, the asymptotic behavior in a neighborhood of the origin has not been studied before. To fill this gap, we should impose a Cauchy integral, which is the uniformly bounded solution to a scalar Riemann-Hilbert problem, and which converges exponentially fast (a...

Using the steepest descent method of Deift-Zhou, we derive locally uniform asymptotic formulas for the Meixner polynomials. These include an asymptotic formula in a neighborhood of the origin, a result which as far as we are aware has not yet been obtained previously. This particular formula involves a Cauchy integral, which is the uniformly bounded solution to a scalar Riemann-Hilbert problem,...

I. The Complex Number System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 II. Elementary Properties and Examples of Analytic Fns. . . . . . . . . . . . . . . . 3 Differentiability and analyticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 The Logarithm . . . . . . . . . . . . . . . . . . . . . . . . . . ...

We introduce a hierarchy of integrable partial differential equations in 2 + 1 dimensions arising from the commutation of 2 dimensional vector fields, and we construct the formal solution of the associated Cauchy problems using the Inverse Scattering Transform for one-parameter families of vector fields recently introduced in [1, 2]. Due to the ring property of the space of eigenfunctions, the ...

In this paper, we present recent results in integral inequality theory. Our results are based on thefractional integration in the sense of Riemann-Liouville

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.

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...

The solution of the Riemann problem was a building block for general Cauchy problems in conservation laws. A Cauchy problem is approximated by a series of Riemann problems in many numerical schemes. But, since the structure of the Riemann solution holds locally in time only, and, furthermore, a Riemann solution is not piecewise constant in general, there are several fundamental issues in this a...