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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 collocation methods for fractional multipantograph delay differential equations*
In this paper, we propose and analyze a spectral collocation method for the numerical solutions of fractional multipantograph delay differential...
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Convergence analysis for delay Volterra integral equation
In this article we use Chebyshev spectral collocation method to deal with the Volterra integral equation which has two kinds of delay items. We use...
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Bounded Solutions of Functional Integro-Differential Equations Arising from Heat Conduction in Materials with Memory
In this paper, we consider recurrent behavior of bounded solutions for a functional integro-differential equation arising from heat conduction in...
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Nonlinear convolution integro-differential equation with variable coefficient
For an integro-differential equation of the convolution type defined on the half-line [0, ∞) with a power nonlinearity and variable coefficient, we...
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A fast time domain solver for the equilibrium Dyson equation
We consider the numerical solution of the real-time equilibrium Dyson equation, which is used in calculations of the dynamical properties of quantum...
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Numerical solutions of two-dimensional nonlinear integral equations via Laguerre Wavelet method with convergence analysis
In this paper, the approximate solutions for two different type of two-dimensional nonlinear integral equations: two-dimensional nonlinear...
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A fast and oblivious matrix compression algorithm for Volterra integral operators
The numerical solution of dynamical systems with memory requires the efficient evaluation of Volterra integral operators in an evolutionary manner....
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A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels
We present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure...
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A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law
We consider a fractional order viscoelasticity problem modelled by a power-law type stress relaxation function. This viscoelastic problem is a...
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Spectral collocation method for nonlinear Caputo fractional differential system
A spectral collocation method is developed to solve a nonlinear Caputo fractional differential system. The main idea is to solve the corresponding...
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On Compactness of Regular Integral Operators in the Space L1
In this paper we obtain a sufficient condition for quite continuity of Fredholm type integral operators in the space L 1 ( a, b ). Uniform approximations...
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Operational Calculus for the General Fractional Derivative and Its Applications
In this paper, we first address the general fractional integrals and derivatives with the Sonine kernels that possess the integrable singularities of...
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Operational Method for Solving Fractional Differential Equations with the Left-and Right-Hand Sided Erdélyi-Kober Fractional Derivatives
In this paper, we first provide a survey of some basic properties of the left-and right-hand sided Erdélyi-Kober fractional integrals and derivatives...
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On representation and interpretation of Fractional calculus and fractional order systems
In this work a relationship between Fractional calculus (FC) and the solution of a first order partial differential equation (FOPDE) is suggested....
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Thermal Blow-up in a Finite Strip with Superdiffusive Properties
We investigate the problem of a high-energy source localized within a one-dimensional superdiffusive medium of finite length. The problem is modeled...
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Spectral collocation method for system of weakly singular Volterra integral equations
Based on our previous research, we investigate spectral collocation method for system of weakly singular Volterra integral equations. The provided...
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On Integral Equations the Kernels of Which are Homogeneous Functions of Degree (−1)
The present paper deals with integral equations the kernels of which are homogeneous functions of degree (−1). Factorization approach to such...
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A Local Galerkin Integral Equation Method for Solving Integro-differential Equations Arising in Oscillating Magnetic Fields
The current work investigates a computational method to solve a class of integro-differential equations which describes the charged particle motion...
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Global Solutions to Stochastic Volterra Equations Driven by Lévy Noise
In this paper we investigate the existence and uniqueness of semilinear stochastic Volterra equations driven by multiplicative Lévy noise of pure...