Results 61 to 70 of about 243 (176)

Solvability of some integral equations in Hilbert spaces

Electronic Journal of Differential Equations, 2004
We consider an integral equation of Fredholm and Volterra type with spectral parameter depending on time. Conditions of solvability are established when the initial value of the parameter coincides with an eigenvalue of Fredholm operator.
Onur Alp Ilhan
doaj  

Approximate Solution of Intuitionistic Fuzzy Volterra Integral Equation of Separable‐Type Kernel Using Elzaki Adomian Decomposition Method

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, Saleem Abdullah, Samuel Okyere, Bikash Koli Dey   +3 more
wiley   +1 more source

A Projection Method for Solving Nonlinear Volterra-Fredholm Integral Equations using Legendre Hybrid Functions

Journal of Mathematical Extension, 2013
Since various problems in science and engineering fields can be modeled by nonlinear Volterra-Fredholm integral equations, the main focus of this study is to present an effective numerical method for solving them.
M. Roodaki, Z. JafariBehbahani
doaj  

Numerical solution of special 2D Fredholm-Volterra integral equations using barycentric Gegenbauer interpolation collocation method

Journal of Physics: Conference Series, 2020
Abstract In this paper, an efficient collocation method based on two dimensional barycentric Gegenbauer interpolation is used to solve a kind of special two dimensional Fredholm-Volterra integral equations (2D-FVIEs). The explicit barycentric weights for the Gegenbauer-Gauss nodes not only reduce the complicated calculation but also ...
Hongyan Liu, Jin Huang
openaire   +1 more source

An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
This article extends a spectral collocation approach based on Lucas polynomials to numerically solve the integrodifferential equations of both Volterra and Fredholm types for multi–higher fractional order in the Caputo sense under the mixed conditions. The new approach focusses on using a matrix strategy to convert the supplied equation with conditions
Shabaz Jalil Mohammedfaeq, Miran Bayan Mohammed Amin, Dashne Chapuk Zahir, Shazad Shawki Ahmed, Saeid Abbasbandy   +4 more
wiley   +1 more source

An accelerated iterative technique for solving mixed Fredholm-Volterra integral equations

Ain Shams Engineering Journal
In this paper, we propose an accelerated numerical technique for solving mixed Fredholm-Volterra integral equations (MFVIEs). The MFVIE is solved using the two-grid iterative technique, which uses a small system of equations to reach higher accuracy. The convergence analysis showed that using this technique reduces computational costs by 85% compared ...
A.G. Attia, I.L. El-kalla, A. Elsaid, R.A. Abd El-Monem   +3 more
openaire   +2 more sources

An Analytical‐Numerical Method for the Solution of Nonlinear Fractional Fredholm Integro‐Differential Equations With Logarithmic Weakly Singular Kernel

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this work, we investigate a numerical method for solving nonlinear fractional Fredholm integro‐differential equations with logarithmic weakly singular kernels. Since the direct solution of these equations using classical methods results in low accuracy and high computational cost due to the singular behavior of the exact solution at both endpoints ...
Ali Edham Awadh, Esmaeil Najafi, Guotao Wang   +2 more
wiley   +1 more source

An Analytical Approach to Solve a System of 2D Nonlinear Volterra–Fredholm Integral Equations on Nonrectangular Domains Based on Radial Basis Functions

Journal of Mathematics, Volume 2025, Issue 1, 2025.
We aim to introduce a numerical method to solve a system of two‐dimensional nonlinear integral equations of Volterra–Fredholm type with the second kind on nonrectangular domains. The method estimates the solutions of the system by a discrete collocation method based on radial basis functions constructed on scattered points.
Mohsen Jalalian, Manochehr Kazemi, Mohammad Esmael Samei, Chang Phang   +3 more
wiley   +1 more source

The study of the solution of a Fredholm-Volterra integral equation by Picard operators [PDF]

Studia Universitatis Babes-Bolyai Matematica, 2019
In this paper we will use the Picard operators technique, in order to establish the existence and uniqueness, data dependence and Gronwall-type results for the solutions of a Fredholm-Volterra functional-integral equation. The paper ends with a result of the Ulam-Hyers stability of this integral equation.
openaire   +1 more source

Existence and optimal control results for Caputo fractional delay Clark's subdifferential inclusions of order r∈(1,2) with sectorial operators

Optimal Control Applications and Methods, Volume 45, Issue 4, Page 1832-1850, July/August 2024.
The graphical abstract delves into Caputo fractional nonlinear differential inclusions, highlighting their complexities and the need for innovative solutions. We propose a mild solution approach to address these challenges efficiently. Our investigation focuses on determining the existence of mild solutions under varied conditions and exploring optimal
Marimuthu Mohan Raja, Velusamy Vijayakumar, Kalyana Chakravarthy Veluvolu, Anurag Shukla, Kottakkaran Sooppy Nisar   +4 more
wiley   +1 more source