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Properties of Solutions to Volterra-Type Integro-Differential Equations
AbstractIn the present work, it is considered the features of solving classical Volterra-type integro-differential equations. Considered: features of...
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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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Two-Point Boundary Value Problem for Volterra–Fredholm Integro-Differential Equations and Its Numerical Analysis
AbstractA two-point boundary value problem for Volterra–Fredholm integro-differential equations is considered. To solve this problem, Dzhumabaev...
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Fractional Linear Volterra Integro-Differential Equations in Banach Spaces
The paper presents the foundations of the theory of linear fractional Volterra integro-differential equations of convolution type in Banach spaces....
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Spectral Analysis of the Generators for Semigroups Associated with Volterra Integro-Differential Equations
AbstractThe paper studies the properties of a linear operator that is the generator of a semigroup associated with Volterra integro-differential...
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Well-Posed Solvability of Volterra Integro-Differential Equations in Hilbert Spaces
AbstractWe study the well-posed solvability of initial value problems for Volterra integro-differential equations in a Hilbert space with kernels of...
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Abstract degenerate Volterra integro-differential equations: inverse generator problem
In this paper, we investigate the inverse generator problem for abstract degenerate Volterra integro-differential equations in locally convex spaces....
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Application of Semigroup Theory to the Study of Volterra Integro-Differential Equations
AbstractWe study abstract Volterra integro-differential equations, which are operator models of problems in the theory of viscoelasticity. The class...
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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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Volterra-Type Integro-Differential Equations with Two-Point Singular Differential Operator
AbstractFirst-order Volterra-type integro-differential equations with a two-point singular differential operator are considered. For this class of...
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Delay Differential Equations with Differentiable Solution Operators on Open Domains in C((−∞, 0], ℝn) and Processes for Volterra Integro-Differential Equations
For autonomous delay differential equations x ′( t ) = f ( x t ) we construct a continuous semiflow of continuously differentiable solution operators x 0 ↦ x t ...
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Investigation of Integro-Differential Equations by Methods of Spectral Theory
This paper provides a survey of results devoted to the study of integro-differential equations with unbounded operator coefficients in a Hilbert...
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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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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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Some Classes of First-Order Integro-Differential Equations and Their Conjugate Equations
AbstractThe paper is devoted to the investigation of some classes of first-order integro-differential equation with singular kernel and its conjugate...
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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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The Uniform Convergence of a DG Method for a Singularly Perturbed Volterra Integro-Differential Equation
The purpose of this work is to implement a discontinuous Galerkin (DG) method with a one-sided flux for a singularly perturbed Volterra...
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On the Properties of the Generators of Semigroups Associated with Volterra Integro-Differential Equations
AbstractThe paper studies the properties of a linear operator that is the generator of a semigroup associated with Volterra integro-differential...
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Hyers–Ulam stability of impulsive Volterra delay integro-differential equations
This paper discusses different types of Ulam stability of first-order nonlinear Volterra delay integro-differential equations with impulses. Such...