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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, Rogelio Grau, Carlos Lizama, Jaqueline Mesquita   +3 more
doaj   +4 more sources

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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Fractional Behaviours Modelling with Volterra Equations: Application to a Lithium-Ion Cell and Comparison with a Fractional Model

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, Christophe Farges, Jocelyn Sabatier   +2 more
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Stability theory for Volterra equations

Journal of Differential Equations, 1979
T. A. Burton
openalex   +3 more sources

Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation.

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, A K Amin, M A Abdelkawy, A A Alluhaybi, I Hashim   +4 more
doaj   +1 more source

Existence and global attractivity of periodic solution for impulsive stochastic Volterra-Levin equations

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
doaj   +1 more source

The Stochastic Volterra Equation [PDF]

, 1993
We study the stochastic (Skorohod) integral equation of the Volterra type $$ {X_t}(\omega ) = {Y_t}(\omega ) + \int\limits_0^t {b(t,s){X_s}(\omega )ds} + \int\limits_0^t {\sigma (t,s){X_s}(\omega )\delta {B_s}(\omega )} $$ where Y, b and a are given functions; b and a are bounded, deterministic and Yt is stochastic, not necessarily adapted.
Øksendal, Bernt, Zhang, Tusheng
openaire   +3 more sources

Comparison of Stochastic Volterra Equations [PDF]

Bernoulli, 2000
Let (Q,, Y, , {Yt: t > 0}, P) be a probability space with the filtration satisfying the usual hypotheses. For each j = 1, ..., n, let {Mj(t)} be a real-valued continuous local martingale adapted to (Yt), and { Vj(t)} be a continuous ('t)-adapted process, each with paths of bounded variation on compacts.
Ferreyra, Guillermo, Sundar, Padamanbhan
openaire   +3 more sources

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, Józef Banaś, Raina Bekmoldayeva   +2 more
doaj   +1 more source

Integral Equations Related to Volterra Series and Inverse Problems: Elements of Theory and Applications in Heat Power Engineering

Mathematics, 2021
The paper considers two types of Volterra integral equations of the first kind, arising in the study of inverse problems of the dynamics of controlled heat power systems.
Svetlana Solodusha, Mikhail Bulatov
doaj   +1 more source