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2015, ISBN 1482254301, xxv, 458
The theory of linear Volterra integro-differential equations has been developing rapidly in the last three decades. This book provides an easy to read concise... 
Volterra equations | Integro-differential equations | Mathematics
Book
Publicacions Matemàtiques, ISSN 0214-1493, 1/2014, Volume 58, Issue 1, pp. 133 - 154
Aim of this paper is to show that weak solutions of the following fractional Laplacian equation $\left\{ {_{u = g}^{{{\left( { - \Delta } \right)}^s}u =... 
Regularity theory | Weak solutions | Fractional Laplacian | Integrodifferential operators | Viscosity solutions | MATHEMATICS | regularity theory | fractional Laplacian | weak solutions | INTEGRODIFFERENTIAL EQUATIONS | viscosity solutions | OPERATORS | 35R09 | 49N60 | 35D30 | 45K05
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2018, Volume 56, Issue 1, pp. 1 - 23
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 06/2019, Volume 267, Issue 1, pp. 547 - 586
We prove some regularity estimates for viscosity solutions to a class of possible degenerate and singular integro-differential equations whose leading operator... 
Double phase functionals | Quasilinear nonlocal operators | Hölder continuity | Fractional Sobolev spaces | Viscosity solutions | MATHEMATICS | Holder continuity | INTEGRODIFFERENTIAL EQUATIONS | ELLIPTIC-EQUATIONS | MINIMIZERS
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 04/2013, Volume 81, pp. 70 - 86
The fractional stochastic differential equations have wide applications in various fields of science and engineering. This paper addresses the issue of... 
Existence result | Fractional stochastic differential equation | Resolvent operators | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRODIFFERENTIAL EQUATIONS | EVOLUTION INCLUSIONS | MILD SOLUTIONS | Differential equations
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2019, Volume 371, Issue 5, pp. 3417 - 3450
Let X=(X_t)_{t \ge 0} be a stochastic process which has a (not necessarily stationary) independent increment on a probability space (\Omega , \mathbb{P}). In... 
Diffusion equation for jump process | Pseudo-differential operator | theory | Non-stationary increment | MATHEMATICS | pseudo-differential operator | INTEGRODIFFERENTIAL EQUATIONS | non-stationary increment | OPERATORS | L-p-theory
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 4/2011, Volume 200, Issue 1, pp. 59 - 88
We obtain C 1,α regularity estimates for nonlocal elliptic equations that are not necessarily translation-invariant using compactness and perturbative methods... 
Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | INTEGRODIFFERENTIAL EQUATIONS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 382, Issue 1, pp. 426 - 447
We consider initial value/boundary value problems for fractional diffusion-wave equation: ∂ t α u ( x , t ) = L u ( x , t ) , where 0 < α ⩽ 2 , where L is a... 
Fractional diffusion equation | Initial value/boundary value problem | Well-posedness | Inverse problem | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRODIFFERENTIAL EQUATION | HEAT-EQUATION | Universities and colleges
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 05/2018, Volume 63, Issue 5, pp. 1517 - 1522
In this paper, we study the quadratic regulator problem for a process governed by a Volterra integrodifferential equation in ℝ n . Our main goal is the proof... 
Regulators | Integrodifferential equations | Riccati equations | Integral equations | Optimal control | Process control | Differential equations | Riccati equation | optimal control | STRUCTURAL OPERATOR-F | RETARDED-SYSTEMS | BOUNDARY CONTROL-SYSTEMS | THEOREM | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 11/2018, Volume 337, pp. 452 - 460
In this work we prove that a family of explicit numerical methods is convergent when applied to a nonlinear Volterra equation with a power-type nonlinearity.... 
Nonlinearity | Numerical method | Power-type | Volterra equation | GRONWALL INEQUALITY | EXISTENCE | MATHEMATICS, APPLIED | APPROXIMATION | NONTRIVIAL SOLUTIONS | INTEGRAL-EQUATIONS | INTEGRODIFFERENTIAL EQUATIONS | UNIQUENESS | OPERATOR
Journal Article
Applied Mathematical Modelling, ISSN 0307-904X, 09/2015, Volume 39, Issue 17, pp. 5121 - 5130
•A method based on Chebyshev wavelet expansion has been proposed.•The proposed method is well suited for fractional Sawada–Kotera equation.•The results of this... 
Caputo derivative | Fractional Sawada–Kotera equation | Chebyshev wavelet method | Homotopy analysis method | Fractional sawada-kotera equation | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | INTEGRODIFFERENTIAL EQUATIONS | TIME | Fractional Sawada-Kotera equation
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2016, Volume 38, Issue 1, pp. A146 - A170
Journal Article