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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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Volterra Equations Driven by Semimartingales
Annals of Probability, 1985 In modelling systems corrupted by noise, stochastic integral equations of Volterra type arise. \textit{M. A. Berger} and \textit{V. J. Mizel} [J. Integral Equations 2, 187-245 and 319-337 (1980; Zbl 0442.60064 and Zbl 0452.60073, resp.)] handled the white noise case and conjectured that their results could be extended to the case when Brownian motion ...
exaly +4 more sources
Some new results on interval-valued volterra integro-differential equations for caputo fractional derivative [PDF]
Scientific ReportsVolterra integro differential equations are one of the necessary tools to discuss the framework of modeling systems with memory and nonlinear behaviors comprehensively, which commonly appear in several engineering and scientific applications.
Saima Noureen +2 more
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Fuzzy Optimization and Modeling, 2022 In this study, we consider solving the second kind Volterra fuzzy integral equations system in two cases linear and nonlinear by using a semi-analytic method, called Differential Transform Method (DTM).
Mahmoud Paripour, Mandana Takrimi
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Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations
Discrete Dynamics in Nature and Society, 2021 Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general ...
Yunfei Li, Shoufu Li
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Fractal and Fractional, 2022 This paper proposes to model fractional behaviors using Volterra equations. As fractional differentiation-based models that are commonly used to model such behaviors exhibit several drawbacks and are particular cases of Volterra equations (in the kernel ...
Vincent Tartaglione +2 more
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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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Electronic Journal of Qualitative Theory of Differential Equations, 2012 In this paper, we consider a class of impulsive stochastic Volterra-Levin equations. By establishing a new integral inequality, some sufficient conditions for the existence and global attractivity of periodic solution for impulsive stochastic Volterra ...
dingshi li, Daoyi Xu
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A Unified Approach to Some Classes of Nonlinear Integral Equations
Journal of Function Spaces, 2014 We are going to discuss some important classes of nonlinear integral equations such as integral equations of Volterra-Chandrasekhar type, quadratic integral equations of fractional orders, nonlinear integral equations of Volterra-Wiener-Hopf type, and ...
Nurgali K. Ashirbayev +2 more
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Comparison of Stochastic Volterra Equations [PDF]
Bernoulli, 2000 The authors prove a pathwise comparison theorem for solutions of the following one-dimensional stochastic Volterra equations: \[ X_i(t)=\xi_i + \sum_{j=1}^n H(t)\int_0^t \sigma_j(s,X_i(s)) dM_j(s) + \sum_{j=1}^n \int_0^t b_j^i(t,s,X_i(s)) dV_j(s),\quad i=1,2, \] where \(\{H(t)\}\) is a continuous adapted positive and strictly decreasing process ...
Ferreyra, Guillermo, Sundar, Padamanbhan
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