Fredholm integral equation
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A perturbation-based approach for solving fractional-order Volterra–Fredholm integro differential equations and its convergence analysis Open
[EN]The present work considers the approximation of solutions of a type of fractional-order Volterra–Fredholm integro-differential equations, where the fractional derivative is introduced in Caputo sense. In addition, we also present sever…
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Backstepping-Forwarding Control and Observation for Hyperbolic PDEs With Fredholm Integrals Open
International audience
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Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis Open
This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. Th…
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Convergence of 2D-orthonormal Bernstein collocation method for solving 2D-mixed Volterra–Fredholm integral equations Open
In this paper, an efficient numerical method is used for solving 2D-mixed Volterra–Fredholm integral equations. This method is based on 2D-orthonormal Bernstein polynomials (2D-OBPs) together with collocation method. This approach is appli…
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Optimal control problems of forward-backwardstochastic Volterra integral equations Open
Optimal control problems of forward-backward stochastic Volterraintegral equations (FBSVIEs, in short) are formulated and studied. Ageneral duality principle is established for linear backwardstochastic integral equation and linear stochas…
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The Approximate Solutions of Fractional Volterra-Fredholm Integro-Differential Equations by using Analytical Techniques Open
This paper demonstrates a study on some significant latest innovations in the approximation techniques to find the approximate solutions of Caputo fractional Volterra-Fredholm integro-differential equations. To apply this, the study uses A…
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Explicit equilibrium solutions for the aggregation equation with power-law potentials Open
Despite their wide presence in various models in the study of collective behaviors, explicit swarming patterns are difficult to obtain. In this paper, special stationary solutions of the aggregation equation with power-law kernels are cons…
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$\Bbb Z_{2}$-indices and factorization properties of odd symmetric Fredholm operators Open
A bounded operator T on a separable, complex Hilbert space is said to be odd symmetric if I^*T^{t}I=T where I is a real unitary satisfying I^{2}=-1 and T ^t denotes the transpose of T . It is proved that such an operator can always be fact…
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Usage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-differential equation of the second kind Open
The reliability of the homotopy analysis method (HAM) and reduction in the size of the computational work give this method a wider applicability. In this paper, HAM has been successfully applied to find the approximate solutions of Caputo …
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A Computational Technique for Solving Three-Dimensional Mixed Volterra–Fredholm Integral Equations Open
In this article, a novel and efficient approach based on Lucas polynomials is introduced for solving three-dimensional mixed Volterra–Fredholm integral equations for the two types (3D-MVFIEK2). This method transforms the 3D-MVFIEK2 into a …
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On analysis of the fuzzy fractional order Volterra-Fredholm integro-differential equation Open
In this paper, we study the fractional integro-differential equation under the notion of fuzziness. We consider the fuzzy fractional Volterra-Fredholm integro-differential equation in the Caputo sense and show its existence and uniqueness …
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Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation Open
We analyse the case of a dense modified Korteweg–de Vries (mKdV) soliton gas and its large time behaviour in the presence of a single trial soliton. We show that the solution can be expressed in terms of Fredholm determinants as well as in…
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Homotopy Analysis Method for the First Order Fuzzy Volterra-Fredholm Integro-differential Equations Open
A fuzzy Volterra-Fredholm integro-differential equation (FVFIDE) in a parametric case is converted to its related crisp case. We use homotopy analysis method to find the approximate solution of this system and hence obtain an approximation…
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THE RELIABLE MODIFIED OF LAPLACE ADOMIAN DECOMPOSITION METHOD TO SOLVE NONLINEAR INTERVAL VOLTERRA-FREDHOLM INTEGRAL EQUATIONS Open
In this paper, we propose a combined form for solving nonlinear interval Volterra-Fredholm integral equations of the second kind based on the modifying Laplace Adomian decomposition method. We find the exact solutions of nonlinear interval…
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A <span>Riemann‐Hilbert</span> Approach to the Lower Tail of the <span>Kardar‐Parisi‐Zhang</span> Equation Open
Fredholm determinants associated to deformations of the Airy kernel are closely connected to the solution to the Kardar‐Parisi‐Zhang (KPZ) equation with narrow wedge initial data, and they also appear as largest particle distributions in m…
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The steady aerodynamics of aerofoils with porosity gradients Open
This theoretical study determines the aerodynamic loads on an aerofoil with a prescribed porosity distribution in a steady incompressible flow. A Darcy porosity condition on the aerofoil surface furnishes a Fredholm integral equation for t…
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Fredholm operators and essential S-spectrum in the quaternionic setting Open
For bounded right linear operators, in a right quaternionic Hilbert space with a left multiplication defined on it, we study the approximate S-point spectrum. In the same Hilbert space, then we study the Fredholm operators and the Fredholm…
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A Solution of Fredholm Integral Equation by Using the Cyclic η s q -Rational Contractive Mappings Technique in b-Metric-Like Spaces Open
In this article, the notion of cyclic η s q -rational contractive mappings is discussed and some fixed point theorems in the context of complete b-metric-like spaces are showed. Here, the obtained consequences unify, extend and generalize …
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Effects of modal dispersion on few-photon–qubit scattering in one-dimensional waveguides Open
We study one- and two-photon scattering from a qubit embedded in a one-dimensional waveguide in the presence of modal dispersion. We use a resolvent based analysis and utilize techniques borrowed from the Lee model studies. Modal dispersio…
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A Study of Some Iterative Methods for Solving Fuzzy Volterra-Fredholm Integral Equations Open
This paper mainly focuses on the recent advances in the some approximated methods for solving fuzzy Volterra-Fredholm integral equations, namely, Adomian decomposition method, variational iteration method and homotopy analysis method. We c…
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Equilibrium distributions and stability analysis of Gaussian Process State Space Models Open
Gaussian Process State Space Models (GP-SSM) are a data-driven stochastic model class suitable to represent nonlinear dynamics. They have become increasingly popular in non-parametric modeling approaches since they provide not only a predi…
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Numerical solution of nonlinear fuzzy Fredholm integral equations of the second kind using hybrid of block-pulse functions and Taylor series Open
The main purpose of this paper is to introduce a method of successive approximations in terms of a hybrid of Taylor series and a block-pulse function, which is given for solving nonlinear fuzzy Fredholm integral equations of the second kin…
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The Generating Function for the Airy Point Process and a System of Coupled Painlevé II Equations : The Airy Point Process and Coupled Painlevé II Equations Open
For a wide class of Hermitian random matrices, the limit distribution of the eigenvalues close to the largest one is governed by the Airy point process. In such ensembles, the limit distribution of the kth largest eigenvalue is given in te…
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Existence and Uniqueness of the Solution for Volterra-Fredholm Integro-Differential Equations Open
In this article, modified Adomian decomposition method is successfully applies to find the approximate so-
\nlutions of Volterra-Fredholm integro-differential equations. Moreover, we prove the existence and unique-
\nness results and conve…
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Solutions of Fractional Differential Type Equations by Fixed Point Techniques for Multivalued Contractions Open
This paper involves extended b −metric versions of a fractional differential equation, a system of fractional differential equations and two‐dimensional (2D) linear Fredholm integral equations. By various given hypotheses, exciting results…
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Fredholm theory for elliptic operators on quasi‐asymptotically conical spaces Open
We consider the mapping properties of generalized Laplace-type operators ${\mathcal L} = \nabla^* \nabla + {\mathcal R}$ on the class of quasi-asymptotically conical (QAC) spaces, which provide a Riemannian generalization of the QALE manif…
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Integral Equation Methods for Elastance and Mobility Problems in Two Dimensions Open
We present new integral representations in two dimensions for the elastance\nproblem in electrostatics and the mobility problem in Stokes flow. These\nrepresentations lead to resonance-free Fredholm integral equations of the\nsecond kind a…
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Some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two variables and their applications Open
In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear V…
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On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations Open
In this paper, we propose a class of simple numerical methods for approximating solutions of one-dimensional mixed Volterra–Fredholm integral equations of the second kind. These methods are based on fixed point results for the existence an…
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A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle Open
In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of B-spline quasi-affine tight framelet systems generated by the unitary and oblique extensio…