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Riemann-Stieltjes Integral [PDF]
Formalized Mathematics, 2016 In this article, the definitions and basic properties of Riemann-Stieltjes integral are formalized in Mizar [1]. In the first section, we showed the preliminary definition. We proved also some properties of finite sequences of real numbers. In Sec. 2, we
Nakasho, Kazuhisa +2 more
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On the Riemann-Stieltjes Integral [PDF]
Mathematics Interdisciplinary Research, 2022 This study contributes to the theory of Riemann-Stieltjes integral. We prove that if all continuous piecewise linear functions are Riemann-Stieltjes integrable with respect to a bounded integrator α : [a,b] → R, then α must be of bounded variation on [a ...
Ali Parsian
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Advances in Difference Equations, 2020 In this work, the aim is to discuss a new class of singular nonlinear higher-order fractional boundary value problems involving multiple Riemann–Liouville fractional derivatives.
Lishan Liu, Dandan Min, Yonghong Wu
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Infinite point and Riemann–Stieltjes integral conditions for an integro-differential equation
Nonlinear Analysis, 2019 In this paper, we study the existence of solutions for two nonlocal problems of integro-differential equation with nonlocal infinite-point and Riemann–Stieltjes integral boundary conditions. The continuous dependence of the solution will be studied.
Ahmed El-Sayed, Reda Gamal
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Approximating Riemann-Stieltjes Integral Using New Time and Cost Efficient Trapezoid-type Quadrature
European Journal of Pure and Applied MathematicsEngineers and scientists adopt numerical integration to achieve an approximate solution for definite integrals that have no analytic solution. This research focuses on developing some new derivative based quadrature schemes for numerically integrating ...
Kashif Memon +7 more
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Existence Results for Fractional Differential Equations with Multistrip Riemann–Stieltjes Integral Boundary Conditions [PDF]
Discrete Dynamics in Nature and Society, 2018 This paper is concerned with the existence and multiplicity of the positive solutions for a fractional boundary value problem with multistrip Riemann–Stieltjes integral boundary conditions.
Tongling Lv, Huihui Pang, Limei Cao
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SIFAT-SIFAT INTEGRAL RIEMANN-STIELTJES
Barekeng, 2007 If is limited and []ℜ→baf,:[]ℜ→ba,:α Monotone increase in [, is Riemann-Stieltjes integral able to α on ] ba,[]ba, simply written by[]αRSf∈ if . With JI=()()xdxfIbaα∫= is called Riemann Stieltjes lower integral f to α and ()()xdxfJbaα∫
Francis Y. Rumlawang, Harimanus Batkunde
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Nontrivial Solution of Fractional Differential System Involving Riemann-Stieltjes Integral Condition [PDF]
Abstract and Applied Analysis, 2012 We study the existence and uniqueness of nontrivial solutions for a class of fractional differential system involving the Riemann-Stieltjes integral condition, by using the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle,
Ge-Feng Yang
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AxiomsIn this article, we delve into delayed fractional differential equations with Riemann–Stieltjes integral boundary conditions and fractional impulses.
Xiaojun Lv, Kaihong Zhao, Haiping Xie
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Advances in Difference Equations, 2018 This paper studies a system of fractional differential equations with Riemann–Stieltjes integral conditions. The existence and uniqueness of nontrivial solutions to the above system are established under some weaker conditions by the Leray–Schauder ...
Bingmei Liu +3 more
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