In this paper, we establish the existence and uniqueness results to Cauchy problem posed for a fuzzy fractional Volterra-Stieltjes integrodifferential equation. The method of successive approximations is used prove existence, whereas contraction theory applied solution problem.

Necessary and sufficient conditions for the convergence of vector S-fractions are obtained, generalizing classical results of Stieltjes. A class of unbounded difference operators of high order possessing a set of spectral measures is described.

In this paper we present a formula relating Stieltjes numbers γn (1.3) and ηn (1.4). Using it we derive an explicit formula for the oscillating part of Li’s numbers ∼ λn (3.1) which are connected with the Riemann hypothesis.

We show a way to adapt the ideas of Stieltjes to obtain an electrostatic interpretation of the zeroes of a large class of orthogonal polynomials. c © 1998 Elsevier Science B.V. All rights reserved.

Some Ostrowski’s type inequalities for the Riemann-Stieltjes integral R b a f eit du (t) of continuous complex valued integrands f : C (0; 1)! C de…ned on the complex unit circle C (0; 1) and various subclasses of integrators u : [a; b] [0; 2 ] ! C of bounded variation are given. Natural applications for functions of unitary operators in Hilbert spaces are provided as well. 1. Introduction The ...

It has been proposed that the arbitrage possibility in the fractional Black–Scholes model depends on the definition of the stochastic integral. More precisely, if one uses the Wick– Itô–Skorohod integral one obtains an arbitrage-free model. However, this integral does not allow economical interpretation. On the other hand it is easy to give arbitrage examples in continuous time trading with sel...

| In a note at the end of his paper Recherches sur les fractions continues, Stieltjes gave a necessary and suucient condition when a continued fraction is represented by a meromorphic function. This result is related to the study of compact Jacobi matrices. We indicate how this notion was developped and used since Stieltjes, with special attention to the results by M. G. Krein. We also pay atte...

The link between fractional and stochastic calculus established in part I of this paper is investigated in more detail. We study a fractional integral operator extending the Lebesgue–Stieltjes integral and introduce a related concept of stochastic integral which is similar to the so–called forward integral in stochastic integration theory. The results are applied to ODE driven by fractal functi...

We introduce the notion of Stieltjes integral with respect to the spectral measure corresponding to a normal operator. Sufficient conditions for the existence of this integral are given, and estimates for its norm are established. The results are applied to operator Sylvester and Riccati equations. Assuming that the spectrum of a closed densely defined operator A does not have common points wit...

Take a linear ordinary differential operator d(z) = Pk i=1 Qi(z) d dzi with polynomial coefficients and set r = maxi=1,...,k(degQi(z) − i). If d(z) satisfies the conditions: i) r ≥ 0 and ii) degQk(z) = k + r we call it a nondegenerate higher Lamé operator. Following the classical examples of E. Heine and T. Stieltjes we initiated in [6] the study of the following multiparameter spectral problem...