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New General Solution to a Quasilinear Fredholm Integro-Differential Equation and Its Application
AbstractA quasilinear Fredholm integro-differential equation is considered on a finite interval. By using Dzhumabaev parametrization method the...
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An Inverse Problem for a Hyperbolic Integro-Differential Equation in a Bounded Domain
AbstractWe consider the inverse problem of finding the kernel of the integral term in an integro-differential equation. The problem of finding the...
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Inverse Problem for a Non-Homogeneous Integro-Differential Equation of the Hyperbolic Type
AbstractThe inverse problem of determining the solution and one-dimensional kernel of the integral term in an inhomogeneous integro-differential...
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Asymptotic Behavior of Solutions of a Complete Second-Order Integro-Differential Equation
In this paper, we study a complete second-order integro-differential operator equation in a Hilbert space. The difference-type kernel of an integral...
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Analysis of Abstract Partial Impulsive Integro-Differential System with Delay via Integrated Resolvent Operator
In this manuscript, we employ integrated resolvent operator to derive the variation of constants formula for the solution of the impulsive...
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A Novel Uniform Numerical Approach to Solve a Singularly Perturbed Volterra Integro-Differential Equation
AbstractIn this paper, the initial value problem for the second order singularly perturbed Volterra integro-differential equation is considered. To...
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Spectral Properties of the Generator of a Semigroup Generated by the Volterra Integro-Differential Equation
AbstractThe spectral properties of a linear operator that is the generator of a semigroup generated by a Volterra integro-differential equation in a...
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Integro-Differential Equation with a Sum-Difference Kernels and Power Nonlinearity
AbstractSharp a priori estimates are obtained for solutions to a nonlinear Volterra-type integro-differential equation with a sum-difference kernel...
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Inverse Problem of Determining the Kernel of Integro-Differential Fractional Diffusion Equation in Bounded Domain
AbstractIn this paper, an inverse problem of determining a kernel in a one-dimensional integro-differential time-fractional diffusion equation with...
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Approximate Solution of an Inverse Problem for a Singularly Perturbed Integro-Differential Heat Equation
AbstractThe paper considers an inverse problem for a singularly perturbed integro-differential heat equation, which consists in determining the...
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Nonlocal Direct and Inverse Problems for a Second Order Nonhomogeneous Fredholm Integro-Differential Equation with Two Redefinition Data
AbstractThe questions of solvability and construction of solutions of a nonlocal direct and inverse problems for a second-order nonhomogeneous...
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Inverse Problem for an Integro-Differential Wave Equation in a Cylindrical Domain
AbstractIn this paper, for an integro-differential wave equation in a cylindrical domain it is studied an inverse problem of searching the unknown...
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Finding the Two-Dimensional Relaxation Kernel of an Integro-Differential Wave Equation
AbstractWe consider the multidimensional inverse problem of determining the kernel of the integral term in an integro-differential wave equation. In...
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Invariant Manifolds and Global Attractor of the Ginzburg–Landau Integro-Differential Equation
AbstractWe consider a periodic boundary value problem for the complex Ginzburg–Landau integro-differential equation. It can be interpreted as a...
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Existence and Stability of Integro Differential Equation with Generalized Proportional Fractional Derivative
AbstractIn this study, integro-differential equations of arbitrary order are studied. The fractional order is expressed in terms of the
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On Stability and Asymptotic Stability of Solutions for a Linear Fourth Order Volterra Integro-Differential Equation on the Half-Axis
AbstractSufficient conditions for the stability and asymptotic stability of solutions of a linear integro-differential equation of the fourth order...
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Generalized Solutions of Degenerate Integro-Differential Equations in Banach Spaces
In this paper, we present a technique for constructing generalized solutions of the Cauchy problem for abstract integro-differential equations with...
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Semigroups of Operators Generated by Integro-Differential Equations with Kernels Representable by Stieltjes Integrals
Abstract Volterra integro-differential equations with kernels of integral operators representable by Stieltjes integrals are investigated. The...
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Study of Volterra Integro-Differential Equations by Methods of Semigroup Theory
AbstractAbstract Volterra integro-differential equations that are operator models of viscoelasticity problems are investigated. The class of...
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Representation of Solutions of a Certain Integro-Differential Equation and Applications
In this paper, we consider a second-order integro-differential equation with unbounded operator coefficients in a Hilbert space, which is an abstract...