Correct Solvability and Representation of Solutions of Volterra Integrodifferential Equations with Fractional Exponential Kernels

2019 ◽  
Vol 100 (2) ◽  
pp. 467-471 ◽  
Author(s):  
V. V. Vlasov ◽  
N. A. Rautian
Keyword(s):  
Integrodifferential Equations ◽  
Correct Solvability ◽  
Representation Of Solutions

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.

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.

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