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Bayesian polynomial neural networks and polynomial neural ordinary differential equations. [PDF]

PLoS Comput Biol
Fronk C, Yun J, Singh P, Petzold L.
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Error distribution of the Euler approximation scheme for stochastic Volterra equations

Journal of theoretical probability, 2022
The purpose of this paper is to establish the convergence in distribution of the normalized error in the Euler approximation scheme for stochastic Volterra equations driven by a standard Brownian motion, with a kernel of the form $$(t-s)^\alpha $$ ( t ...
D. Nualart, Bhargobjyoti Saikia
semanticscholar   +1 more source

Optimal control results for Sobolev‐type fractional mixed Volterra–Fredholm type integrodifferential equations of order 1 < r < 2 with sectorial operators

Optimal control applications & methods, 2022
The goal of this research is to investigate the issue of existence and optimal control results for fractional mixed Volterra–Fredholm type integrodifferential systems of order ...
M. Mohan Raja, V. Vijayakumar
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On a nonlinear volterra equation

Mathematical Methods in the Applied Sciences, 1986
AbstractNonnegative solutions u of the nonlinear Volterra equation u = a * g(u) (g(0) = 0) in mathematical physics are considered. Under certain assumptions the nonhomogenuous equation u = a * g(u) + ƒ is studied. Some approximations of nonnegative solutions of the homogenuous equation are considered by the nonnegative solutions of the nonhomogenuous ...
W. Okrasiński Wroclaw, E. Meister
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Homogenization for a Volterra Equation

SIAM Journal on Mathematical Analysis, 1986
Les AA. considèrent une équation de Volterra de la forme \[ b_ 0u- div_ x(c*\sigma)=b_ 0u_ 0-\beta *u+H \] où \(c=c(x,t)\) et \(b_ 0=b_ 0(x)\) sont des fonctions positives données, \(\sigma =\sigma (x,\nabla u(x,t))\), \(\beta =\beta (x,t)\) et \(H=H(x,t)\) sont données ainsi que \(u_ 0=u_ 0(x)\).
Attouch, Hedy, Damlamian, Alain
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A Volterra Equation with Parameter

SIAM Journal on Mathematical Analysis, 1973
We discuss the Volterra integral equation $x'(t) + \lambda \int_0^t {a(t - \tau )x(\tau )d\tau = k,\lambda \geq \lambda _0 > 0} $. We find conditions under which solutions are bounded on $\{ 0 \leq t < \infty \} $, uniformly in $\lambda $. We deduce results on the asymptotic behavior of certain Volterra equations in Hilbert space arising, for example ...
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Existence and controllability of nonlocal mixed Volterra‐Fredholm type fractional delay integro‐differential equations of order 1 < r < 2

Numerical Methods for Partial Differential Equations, 2020
In our article, we are primarily concentrating on existence and controllability of nonlocal mixed Volterra‐Fredholm type fractional delay integro‐differential equations of order 1 
W. Kavitha Williams, V. Vijayakumar, R. Udhayakumar, S. K. Panda, K. S. Nisar   +4 more
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Volterra-Type Equations in S ′+

Mathematical Notes, 2004
Necessary and sufficient condition for the unique solvability of Volterra integro-differential equation in \(S\prime _ + \) is given.
Pilipović, Stevan, Stojanović, Mirjana
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