In this paper, boundary value problems of fractional order are converted into an optimal control problems. Then an approximate solution is constructed from translations and dilations of a B-spline function such that the exact boundary conditions are satisfied. The fractional differential operators are taken in the Riemann-Liouville and Caputo sense. Several example are given and the optimal err...

Within the variegated framework of Riemann zeta function and related conjecture (Riemann Hypothesis), we would like to start with a study of some quite disregarded or not much in-deep studied historical aspects concerning Entire Function Theory aspects of Riemann zeta function. This first paper essentially would be the manifesto of such a historical research program whose main points will be in...

In this brief note we bring out the analogy between the arithmetic of elliptic curves and the Riemann zeta-function. · · · The aim of this note is to point out the possibility of developing the theory of elliptic curves so that the arithmetical and analytic aspects are developed in strict analogy with the classical theory of the Riemann zeta-function. This has been triggered by Lemmermeyer’s pe...

All this seems to be started by Georg Friedrich Bernhard Riemann’s original paper whose English translation was included at least in [12], without, however forgetting the enormous influence of Leonhard Euler and his studies on the function now known as the Riemann zeta-function. After this, a huge number of papers is available in the internet on the Riemann hypothesis and the zeta-function. Fur...

in this article, we develop the distributed order fractional hybrid differential equations (dofhdes) with linear perturbations involving the fractional riemann-liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-lipschit...

We are solving the classical Riemann-Hilbert problem of rank N > 1 on the extended complex plane punctured in 2m + 2 points, for N × N quasi-permutation monodromy matrices. Our approach is based on the finite gap integration method applied to study the Riemann-Hilbert by Kitaev and Korotkin [1], Deift, Its, Kapaev and Zhou [2] and Korotkin, [3]. This permits us to solve the Riemann-Hilbert prob...

A two-dimensional Riemann solver is proposed for the solution of hyperbolic systems of conservation laws in two dimensions of space. The solver approximates the solution of a so-called angular two-dimensional Riemann problem as the weighted sum of the solutions of one-dimensional Riemann problems. The weights are proportional to the aperture of the regions of constant state. The two-dimensional...

We continue to investigate the physical interpretation of the Riemann zeta function as a FZZT brane partition function associated with a matrix/gravity correspondence begun in arxiv:0708.0645. We derive the master matrix of the (2, 1) minimal and (3, 1) minimal matrix model. We use it’s characteristic polynomial to understand why the zeros of the FZZT partition function, which is the Airy funct...

We present a Non-relativistic Quantum mechanical model, which exhibits the realization of Riemann Conjecture. The technique depends on exposing the S-wave Jost function at zero energy and in identifying it with the Riemann ξ(s) function following a seminal paper of N. N. Khuri. ∗I dedicate this note to my teacher, George Sudarshan of the University of Texas at Austin We begin by recalling the a...