Let $x$ be a complex number which has positive real part, and $w_1,\ldots,w_N$ rational numbers. We show that $w^s \zeta_N (s, x \ |\ w_1,\ldots, w_N)$ can expressed as finite linear combination of the Hurwitz zeta functions over $\mathbf Q(x)$, where $\zeta_N (s,x is Barnes function $w$ explicitly determined by $w_1,\ldots, w_N$. Furthermore, we give generalizations Kummer's formula on gamma K...

In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value in Banach Spaces. Nonlinear functions f(t,u,v) g(t,u,v) the considered allowed to be at every variable. The here forms integrals. order overcome difficulties arising from s...