Fixed point theorems for Geraghty-type mappings applied to solving nonlinear Volterra-Fredholm integral equations in modular G-metric spaces [PDF]
Arab Journal of Mathematical Sciences, 2021 Purpose – The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces.
Godwin Amechi Okeke, Daniel Francis
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An approximation method for the solution of nonlinear integral equations [PDF]
, 2006 A Chebyshev collocation method has been presented to solve nonlinear integral equations in terms of Chebyshev polynomials. This method transforms the integral equation to a matrix equation which corresponds to a system of nonlinear algebraic equations ...
Akyuz-Dascioglu, A, Yaslan, HC
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A Numerical Method for Solving Stochastic Volterra-Fredholm Integral Equation
Iranian Journal of Mathematical Sciences and Informatics, 2023 Summary: In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-Fredholm integral equation. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original equation.
Momenzade, N. +2 more
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Stochastic Analysis of Gaussian Processes via Fredholm Representation [PDF]
, 2016 We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm representation to a transfer principle and develop stochastic analysis by using it.
Sottinen, Tommi, Viitasaari, Lauri
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On random solutions of Volterra-Fredholm integral equations [PDF]
Pacific Journal of Mathematics, 1983 Existence, uniqueness and boundedness theorems for solutions of the nonlinear stochastic integral equation \[ x(t;\omega)=f(t;\omega)+\int^{t}_{0}a(t,s;\omega)g(s,x(s;\omega))ds+\i nt^{\infty}_{0}b(t,s;\omega)h(s,x(s;\omega))ds,\quad t\geq 0 \] are obtained using the admissibility theory of integral operators and contractor theory.
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Evans function and Fredholm determinants [PDF]
, 2014 We explore the relationship between the Evans function, transmission coefficient and Fredholm determinant for systems of first order linear differential operators on the real line.
Karambal, Issa, Malham, Simon J. A
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An approach of extrapolation methods for the solution of nonlinear Volterra–Fredholm integral equations of the second kind [PDF]
Iranian Journal of Numerical Analysis and OptimizationThis study presents the process of using extrapolation methods to solve the nonlinear Volterra–Fredholm integral equations of the second kind. To do this, by approximating the integral terms contained in equations by a quadrature rule, the nonlinear ...
H. Safdari +2 more
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Fractal and Fractional, 2020 The main goal of the paper is to present an approximate method for solving of a two-dimensional nonlinear Volterra-Fredholm fuzzy integral equation (2D-NVFFIE). It is applied the homotopy analysis method (HAM).
Atanaska Georgieva, Snezhana Hristova
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A Jost-Pais-type reduction of (modified) Fredholm determinants for semi-separable operators in infinite dimensions [PDF]
, 2014 We study the analog of semi-separable integral kernels in $\mathcal{H}$ of the type $$ K(x,x')=\begin{cases} F_1(x)G_1(x ...
Gesztesy, Fritz, Nichols, Roger
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Al'brekht's Method in Infinite Dimensions [PDF]
, 2020 In 1961 E. G. Albrekht presented a method for the optimal stabilization of smooth, nonlinear, finite dimensional, continuous time control systems.
Krener, AJ
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