In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses Caputo fractional derivative function with respect to another function, supplemented Riemann–Stieltjes integral conditions. The unique solution is obtained via Banach’s contraction mapping principle, while an result established using Leray–Schauder...

In this article, we study the local behaviour of multiple zeta functions at integer points and write down a Laurent type expansion around these points. Such an involves convergent power series whose coefficients are obtained by regularisation process, similar to one used in defining classical Stieltjes constants for Riemann function. We therefore call constants. The remaining part above mention...

— This paper describes a gênerai formulation of the Euler Characteristic Galerkin (ECG) scheme for scalar conservation laws, based on the theory of the Riemann-Stieltjes intégral. The ECG scheme is proved to be equivalent to the projection of Brenier' s transportcollapse operator. For the purpose of getting higher order accuracy, we explore two recovery procedures, namely continuous linear reco...