Initial-boundary value problems for integrable evolution equations with $3 \times 3$ Lax pairs
, 2012 We present an approach for analyzing initial-boundary value problems for integrable equations whose Lax pairs involve $3 \times 3$ matrices. Whereas initial value problems for integrable equations can be analyzed by means of the classical Inverse ...
Lenells, Jonatan
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Homotopy perturbation method for the mixed Volterra–Fredholm integral equations
Chaos, Solitons & Fractals, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Block‐by‐Block Method for Solving Nonlinear Volterra‐Fredholm Integral Equation [PDF]
Mathematical Problems in Engineering, 2010 We consider a nonlinear Volterra‐Fredholm integral equation (NVFIE) of the second kind. The Volterra kernel is time dependent, and the Fredholm kernel is position dependent. Existence and uniqueness of the solution to this equation, under certain conditions, are discussed.
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Toeplitz Matrix Method and Nonlinear Volterra–Fredholm Integral Equation With Hilbert Kernel
Computational and Mathematical Methods, Volume 2025, Issue 1, 2025.This work emphasizes the investigation of the solution to the nonlinear Volterra–Fredholm integral equation (NV‐FIE) and the necessary conditions for a unique solution. The first step is to convert the NV‐FIE into a system of nonlinear Fredholm integral equations (NFIEs) using the splitting of the time interval. Analytical and semianalytical approaches
Sameeha Ali Raad +2 more
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Solvability of Implicit Fractional Systems With Nonlocal Conditions in Weighted Functional Spaces
International Journal of Differential Equations, Volume 2025, Issue 1, 2025.This paper investigates the existence and uniqueness of solutions for a class of nonlinear implicit Riemann–Liouville fractional integro‐differential equations subject to nonlocal conditions in a weighted Banach space. The inclusion of both implicit effects and nonlocal terms introduces additional complexity, making the analysis both challenging and ...
Abdulrahman A. Sharif +3 more
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A successive iterative approach for two dimensional nonlinear Volterra-Fredholm integral equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2014 In this paper, an iterative scheme for extracting approximate solutions of two dimensional Volterra-Fredholm integral equations is proposed. Considering some conditions on the kernel of the integral equation obtained by discretization of the integral ...
A. H. Borzabadi, M. Heidari
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An exponentially convergent Volterra-Fredholm method for integro-differential equations [PDF]
, 2017 Extending the authors’ recent work [15] on the explicit computation of error bounds for Nystrom solvers applied to one-dimensional Fredholm integro-differential equations (FIDEs), presented herein is a study of the errors incurred by first transforming (
Fairbairn, AI, Kelmanson, MA
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Hybrid functions approach to solve a class of Fredholm and Volterra integro-differential equations
, 2019 In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations.
Bhalekar, Sachin +2 more
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International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.An intuitionistic fuzzy number, which incorporates both membership and nonmembership functions at a same time, allows for a more accurate representation of uncertainty. This work presents an approximate solution to the Volterra integral equation that involves both membership and nonmembership degrees of uncertainty named as intuitionistic fuzzy ...
Zain Khan +3 more
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Fredholm and Volterra nonlinear possibilistic integral equations [PDF]
, 2021 Sorin G. Gal, Ionut T. Iancu
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