The three fundamental properties of the Bernoulli numbers, namely, the theorem of von Staudt-Clausen, von Staudt’s second theorem, and Kummer’s original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients of power series expansion of a higher genus algebraic function with respect to suitable variable. Our generalization strongly ...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. These functions are formed by the hybridi...

In this paper, we study three types of sums of products of ordered Bell and poly-Bernoulli functions and derive their Fourier series expansion. In addition, we express those functions in terms of Bernoulli functions.

In view of a general formula for higher order derivatives the ratio two differentiable functions, authors establish first form Maclaurin power series expansion logarithmic expression in term determinants special Hessenberg matrices whose elements involve Bernoulli numbers. On other hand, comparison, recite and revise second terms Bessel zeta functions

In the paper, forced transverse vibration of fractional viscoelastic Euler-Bernoulli is studied. Based on relationship stress and strain, partial differential equation describing beam considered. The Riemann-Liouville derivative order used. Using Ritz-Galerkin method, transformed into a system equations containing derivatives. dynamic response simply supported to harmonic concentrated force cal...