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Neural Integro-Differential Equations

Proceedings of the AAAI Conference on Artificial Intelligence, 2023
Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these systems are modeled with Integro-Differential Equations (IDEs); generalizations of differential equations that comprise both an
Emanuele Zappala, Antonio Henrique de Oliveira Fonseca, Andrew Henry Moberly, Michael James Higley, Chadi Abdallah, Jessica A. Cardin, David van Dijk   +6 more
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On a New Class of Singular Integro-differential Equations

Қарағанды университетінің хабаршысы. Математика сериясы, 2021
In this paper for a new class of model and non-model partial integro-differential equations with singularity in the kernel, we obtained integral representation of family of solutions by aid of arbitrary functions.
T.K. Yuldashev, S.K. Zarifzoda
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Haar Wavelet Method for the Numerical Solution of Nonlinear Fredholm Integro-Differential Equations [PDF]

مجلة التربية والعلم, 2023
The solution of nonlinear Fredholm integro-differential equations plays a significant role in analyzing many nonlinear events that occur in chemistry, physics, mathematical biology, and a variety of other fields of science and engineering.
Najem A. Mohammad, Younis Sabawi, Mohammad Hasso   +2 more
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On the integro‐differential equations with reflection

Mathematical Methods in the Applied Sciences, 2020
In this paper, by developing important properties on the composition of functions with reflection, using some exponential dichotomy properties and an application of the fixed‐point theorem, several new sufficient conditions for the existence and the uniqueness of an pseudo almost automorphic solutions with measure for some general‐type reflection ...
El Hadi Ait Dads, Safoua Khelifi, Mohsen Miraoui   +2 more
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On the non-uniqueness of the solution to a boundary value problem of heat conduction with a load in the form of a fractional derivative [PDF]

Қарағанды университетінің хабаршысы. Математика сериясы, 2022
The paper deals with the second boundary value problem for the loaded heat equation in the first quadrant.
M.T. Kosmakova, K.A. Izhanova, A.N. Khamzeyeva   +2 more
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On Lp-solvability of stochastic integro-differential equations [PDF]

, 2021
In this thesis, we investigate the Lp-solvability of a class of (possibly) degenerate stochastic integro-differential equations (SIDEs) of parabolic type, which includes the Zakai equation in nonlinear filtering for jump diffusions and the Kolmogorov ...
Wu, Sizhou
core   +1 more source

On Pantograph Integro-Differential Equations

Journal of Integral Equations and Applications, 1994
The authors study the initial value problem for pantograph integro- differential equations of the form \[ y'(t) = a y(t) + \int^ 1_ 0 y(qt) d \mu (q) + \int^ 1_ 0 y'(qt) d \nu (q),\;t > 0, \quad y(0) = y_ 0, \tag{1} \] where \(a\) is a complex constant, \(\mu (q)\) and \(\nu (q)\) are complex-valued functions of bounded variation on \([0,1]\). Denote \(
Iserles, Arieh, Liu, Yunkang
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New applications of the two variable (G′/G, 1/G)-expansion method for closed form traveling wave solutions of integro-differential equations

Journal of Ocean Engineering and Science, 2019
Most fundamental themes in mathematical physics and modern engineering are investigated by the closed form traveling wave solutions of nonlinear evolution equations.
M. Mamun Miah, H.M. Shahadat Ali, M. Ali Akbar, Aly R. Seadawy   +3 more
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The implicit numerical method for the one-dimensional anomalous subdiffusion equation with a nonlinear source term [PDF]

Bulletin of the Polish Academy of Sciences: Technical Sciences, 2021
In the paper, the numerical method of solving the one-dimensional subdiffusion equation with the source term is presented. In the approach used, the key role is played by transforming of the partial differential equation into an equivalent integro ...
Marek Błasik
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A construction of analog of Fredgolm theorems for one class of first order model integro-differential equation with logarithmic singularity in the kernel

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2017
The integral representations of the solution manifold for one class of the first order model integro-differential equation with logarithmic singularity in the kernel are constructed using arbitrary constants. The cases when the given integro-differential
Sarvar K Zaripov
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