Mathematics, 2021 The main aim of this paper is to numerically solve the first kind linear Fredholm and Volterra integral equations by using Modified Bernstein–Kantorovich operators.
Suzan Cival Buranay +2 more
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Volterra–Stieltjes integral equations and impulsive Volterra–Stieltjes integral equations
Electronic Journal of Qualitative Theory of Differential Equations, 2020 In this paper, we prove existence and uniqueness of solutions of Volterra–Stieltjes integral equations using the Henstock–Kurzweil integral. Also, we prove that these equations encompass impulsive Volterra–Stieltjes integral equations and prove the ...
Edgardo Alvarez +3 more
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Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation. [PDF]
PLoS ONE, 2023 A numerical approach based on shifted Jacobi-Gauss collocation method for solving mixed Volterra-Fredholm integral equations is introduced. The novel technique with shifted Jacobi-Gauss nodes is applied to reduce the mixed Volterra-Fredholm integral ...
A Z Amin +4 more
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Approximate solutions to several classes of Volterra and Fredholm integral equations using the neural network algorithm based on the sine-cosine basis function and extreme learning machine [PDF]
Frontiers in Computational Neuroscience, 2023 In this study, we investigate a new neural network method to solve Volterra and Fredholm integral equations based on the sine-cosine basis function and extreme learning machine (ELM) algorithm.
Yanfei Lu +3 more
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Advances in Difference Equations, 2018 This paper aims to obtain an approximate solution for fractional order Riccati differential equations (FRDEs). FRDEs are equivalent to nonlinear Volterra integral equations of the second kind.
Bijan Hasani Lichae +2 more
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Oscillations of Volterra integral equations with delay [PDF]
Tohoku Mathematical Journal, 1993 The oscillatory behavior of the solutions of a Volterra type equation with delay is investigated. Sufficient conditions on the kernel are given which guarantee that the oscillatory character of the forcing term is inherited by the solutions.
George L. Karakostas +2 more
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Numerical solution of nonlinear stochastic Itô–Volterra integral equations based on Haar wavelets
Advances in Difference Equations, 2019 In this paper, an efficient numerical method is presented for solving nonlinear stochastic Itô–Volterra integral equations based on Haar wavelets.
Jieheng Wu, Guo Jiang, Xiaoyan Sang
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On a Volterra Stieltjes integral equation [PDF]
International Journal of Stochastic Analysis, 1990 The paper deals with a study of linear Volterra integral equations involving Lebesgue‐Stieltjes integrals in two independent variables. The authors prove an existence theorem using the Banach fixed‐point principle. An explicit example is also considered.
P. T. Vaz, Sadashiv G. Deo
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On the Maximum Principle for Optimal Control Problems of Stochastic Volterra Integral Equations with Delay [PDF]
Applied Mathematics and Optimization, 2021 In this paper, we prove both necessary and sufficient maximum principles for infinite horizon discounted control problems of stochastic Volterra integral equations with finite delay and a convex control domain.
Yushi Hamaguchi
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Infinite horizon backward stochastic Volterra integral equations and discounted control problems [PDF]
E S A I M: Control, Optimisation and Calculus of Variations, 2021 Infinite horizon backward stochastic Volterra integral equations (BSVIEs for short) are investigated. We prove the existence and uniqueness of the adapted M-solution in a weighted L2space.
Yushi Hamaguchi
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