in this paper, exp-function and (g′/g)expansion methods are presented to derive traveling wave solutions for a class of nonlinear space-time fractional differential equations. as a results, some new exact traveling wave solutions are obtained.

In the present paper, we construct an algorithm for the evaluation of real Riemann zeta function ζ(s) for all real s, s > 1, in polynomial time and linear space on Turing machines in Ko–Friedman model. The algorithms is based on a series expansion of real Riemann zeta function ζ(s) (the series globally convergents) and uses algorithms for the evaluation of real function (1 + x) h and hypergeo-m...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

Generalizations of the Weierstrass formulae to generic surface immersed into R 4 , S 4 and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed.

Generalizations of the Weierstrass formulae to generic surface immersed into R 4 , S 4 and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed.

Generalizations of the Weierstrass formulae to generic surface immersed into R 4 , S 4 and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed.

The Riemann zeta function is a meromorphic functionon the whole complex plane. It has infinitely many zeros and aunique pole at s = 1. Those zeros at s = −2,−4,−6, . . . areknown as trivial zeros. The Riemann hypothesis, conjectured byBernhard Riemann in 1859, claims that all non-trivial zeros of ζ(s)lie on the line R(s) =12 . The density hypothesis is a conjecturede...