Related papers: The Riemann-Stieltjes integral on time scales
We give a proposal to generalize the concept of the differential equations on time scales, such that they can be more appropriate for the analysis of real world problems, and give more opportunities to increase the theoretical depth of…
In this paper we first extend a generalization of Ostrowski type inequality on time scales for functions whose derivatives are bounded and then unify corresponding continuous and discrete versions. We also point out some particular integral…
We introduce the interval Darboux delta integral (shortly, the $ID$ $\Delta$-integral) and the interval Riemann delta integral (shortly, the $IR$ $\Delta$-integral) for interval-valued functions on time scales. Fundamental properties of…
Some properties of the G\"odel space-time metric and its Riemann extension are studied
We study diamond-alpha integrals on time scales. A diamond-alpha version of Fermat's theorem for stationary points is also proved, as well as Rolle's, Lagrange's, and Cauchy's mean value theorems on time scales.
This note states and proves an integral representation formula of the ``variation-of-constant'' type for continuous solutions of linear non-autonomous difference delay systems, in terms of a Lebesgue-Stieltjes integral involving a…
We study the question, whether a Riemann-Stieltjes integral of a positive continuous function with respect to a non-negative function of bounded variation is positive.
We establish some linear and nonlinear integral inequalities of Gronwall-Bellman-Bihari type for functions with two independent variables on general time scales. The results are illustrated with examples, obtained by fixing the time scales…
This essay explores the meaning of stochastic differential equations and stochastic integrals. It sets these subjects in a context of Riemann-Stieltjes integration. It is intended as a comment or supplement to \cite{MTRV}.
Sharp inequalitieis of Gruss type for Stieltjes integrals with application in numerical integration are provided.
We establish some nonlinear integral inequalities for functions defined on a time scale. The results extend some previous Gronwall and Bihari type inequalities on time scales. Some examples of time scales for which our results can be…
This paper deals with the delta continuous Stieltjes variational integral generalized in the plane. In particular, this work presents about some fundamental properties of it. The delta continuous Stieltjes variational integral in the plane…
In this paper, we provide some new generalizations of Feng Qi type integral inequalities on time scales by using elementary analytic methods.
Motivated by the limitations of the traditional definitions of the Riemann-Stieltjes and Darboux-Stieltjes integrals, we introduce a generalized Darboux-Stieltjes integral that is equivalent to an earlier generalization by Ross \cite{Ross}.…
We offer some comments on series involving the M$\ddot{o}$bius function which approximate sums over primes. To accomplish this, we utilize the derivative of the Gram series by applying Riemann-Stieltjes integration. We offer a new formula…
We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…
The Feynman integral is given a stochastic interpretation in the framework of Nelson's stochastic mechanics employing a time-symmetric variant of Nelson's kinematics recently developed by the author.
In this paper, by extending the classic stochastic integrals, we investigate three kinds of more general stochastic integrals: Lebesgue-Stieltjes integrals on predictable sets of interval type (in short: PSITs), stochastic integrals on…
In this paper we first generalize the Ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions. We also point out some particular Ostrowski type inequalities on time scales as special…
The theory of polynomials orthogonal with respect to one inner product is classical. We discuss the extension of this theory to multiple inner products. Examples include the Lam\'e and Heine-Stieltjes polynomials.