Concavity Arguments and Growth Estimates for Linear Integrodifferential Equations in Hilbert Space I. Undamped Equations and Applications to Maxwell Hopkinson Dielectrics.

1977 ◽  
Author(s):  
Frederick Bloom
Keyword(s):  
Hilbert Space ◽  
Integrodifferential Equations

Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Bakka ◽  
S. Hajji ◽  
D. Kiouach
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Hurst Parameter ◽  
Fixed Point Principle ◽  
Stochastic Functional

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.

scholarly journals A Reproducing Kernel Hilbert Space Method for Solving Systems of Fractional Integrodifferential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Samia Bushnaq ◽  
Banan Maayah ◽  
Shaher Momani ◽  
Ahmed Alsaedi
Keyword(s):  
Hilbert Space ◽  
Fractional Calculus ◽  
Present Method ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Nonlinear Problems ◽  
Convergent Series ◽  
Integrodifferential Equations ◽  
Space Method

We present a new version of the reproducing kernel Hilbert space method (RKHSM) for the solution of systems of fractional integrodifferential equations. In this approach, the solution is obtained as a convergent series with easily computable components. Several illustrative examples are given to demonstrate the effectiveness of the present method. The method described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus.

scholarly journals POLYNOMIAL DECAY FOR SOLUTIONS OF HYPERBOLIC INTEGRODIFFERENTIAL EQUATIONS

2008 ◽  
Vol 50 (3) ◽  
pp. 575-581
Author(s):  
T. BÁRTA
Keyword(s):  
Hilbert Space ◽  
Integrodifferential Equation ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Polynomial Decay ◽  
Convolution Kernel ◽  
Linear Integrodifferential Equation

AbstractWe consider a linear integrodifferential equation of second order in a Hilbert space and show that the solution tends to zero polynomially if the decay of the convolution kernel is polynomial. Both polynomials are of the same order.

scholarly journals Investigation of Operator Models Arising in Viscoelasticity Theory

2018 ◽  
Vol 64 (1) ◽  
pp. 60-73
Author(s):  
V V Vlasov ◽  
N A Rautian
Keyword(s):  
Hilbert Space ◽  
Spectral Analysis ◽  
Unbounded Operator ◽  
Integrodifferential Equations ◽  
Abstract Form ◽  
Partial Derivatives ◽  
Correct Solvability ◽  
Operator Functions

We study the correct solvability of initial problems for abstract integrodifferential equations with unbounded operator coefficients in a Hilbert space. We do spectral analysis of operator-functions that are symbols of such equations. The equations under consideration are an abstract form of linear integrodifferential equations with partial derivatives arising in viscoelasticity theory and having a number of other important applications. We describe localization and structure of the spectrum of operatorfunctions that are symbols of such equations.

scholarly journals Nonlinear functional integrodifferential equations in Hilbert space

1999 ◽  
Vol 22 (4) ◽  
pp. 847-854
Author(s):  
J. Y. Park ◽  
S. Y. Lee ◽  
M. J. Lee
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Fundamental Solution ◽  
Bounded Domain ◽  
Smooth Boundary ◽  
Integrodifferential Equations ◽  
Nonlinear Functional ◽  
Integro Differential Equation

LetXbe a Hilbert space and letΩ⊂Rnbe a bounded domain with smooth boundary∂Ω. We establish the existence and norm estimation of solutions for the parabolic partial functional integro-differential equation inXby using the fundamental solution.

scholarly journals An Approximation Method for Solving Volterra Integrodifferential Equations with a Weighted Integral Condition

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
A. Guezane-Lakoud ◽  
N. Bendjazia ◽  
R. Khaldi
Keyword(s):  
Hilbert Space ◽  
Analytical Solution ◽  
Approximation Method ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Integral Condition ◽  
Approximate Solutions ◽  
Integrodifferential Equations ◽  
Numerical Examples ◽  
Weighted Integral

We apply the reproducing kernel Hilbert space (RKHS) method for getting analytical and approximate solutions for second-order hyperbolic integrodifferential equations with a weighted integral condition. The analytical solution is represented in the form of series; thus, then-terms approximate solutions are obtained. The results of the numerical examples are compared with the exact solutions to illustrate the accuracy and the effectivity of this method.

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