Results 21 to 30 of about 341 (180)

On the Volterra integral equation with weakly singular kernel [PDF]

Mathematica Bohemica, 2006
Summary: We give sufficient conditions for the existence of at least one integrable solution of equation \(x(t)=f(t)+\int _{0}^{t} K(t,s)g(s,x(s))\,ds\). Our assumptions and proofs are expressed in terms of measures of noncompactness.
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An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method

International Journal of Differential Equations, 2018
An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method (FDTM).
Rezvan Ghoochani-Shirvan, Jafar Saberi-Nadjafi, Morteza Gachpazan   +2 more
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Regularized Asymptotic Solutions of a Singularly Perturbed Fredholm Equation with a Rapidly Varying Kernel and a Rapidly Oscillating Inhomogeneity

Axioms, 2022
This article investigates an equation with a rapidly oscillating inhomogeneity and with a rapidly decreasing kernel of an integral operator of Fredholm type.
Dana Bibulova, Burkhan Kalimbetov, Valeriy Safonov   +2 more
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Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation

Journal of Mathematics, 2022
This paper deals with the numerical solution of the Abel integral equation based on Müntz–Legendre wavelets. To this end, the Abel integral operator is represented by Müntz–Legendre wavelets as an operational matrix.
Ioannis Dassios, Fairouz Tchier, F. M. O. Tawfiq   +2 more
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To the solution of one pseudo-Volterra integral equation

Қарағанды университетінің хабаршысы. Математика сериясы, 2019
In this paper, we study a homogeneous singular integral Volterra equation of the second kind (pseudoVolterra integral equation). The singularity of the integral equation is shown. Properties of its kernel are proved.
M.T. Jenaliyev, M.I. Ramazanov, M.T. Kosmakova, A.O. Tanin   +3 more
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Approximation Solution of Fuzzy Singular Volterra Integral Equation by Non-Polynomial Spline

Ibn Al-Haitham Journal for Pure and Applied Sciences, 2023
A non-polynomial spline (NPS) is an approximation method that relies on the triangular and polynomial parts, so the method has infinite derivatives of the triangular part of the NPS to compensate for the loss of smoothness inherited by the polynomial. In
Zahraa A. Ibrahim, Nabaa N. Hasan
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The Müntz–Legendre Wavelet Collocation Method for Solving Weakly Singular Integro-Differential Equations with Fractional Derivatives

Fractal and Fractional, 2023
We offer a wavelet collocation method for solving the weakly singular integro-differential equations with fractional derivatives (WSIDE). Our approach is based on the reduction of the desired equation to the corresponding Volterra integral equation.
Haifa Bin Jebreen
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Fredholm and Volterra integral equations with integrable singularities

Hokkaido Mathematical Journal, 2004
The authors present a number of results on the existence of continuous nonnegative solutions \(y\) of the Fredholm equation \[ y(t) = \int_J k(t,s) f(s,y(s))\,ds, \quad t \in J, \tag{F} \] where either \(J = [0,1]\) or \(J = [0,\infty)\), and for the Volterra equation \[ y(t) = \int_0^t k(t,s) f(s,y(s))\,ds, \quad t \in [0,T].
AGARWAL, Ravi P., O'REGAN, Donal
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Collocation Solutions of a Weakly Singular Volterra Integral Equation

Trends in Computational and Applied Mathematics, 2007
The discrete superconvergence properties of spline collocation solutions for a certain Volterra integral equation with weakly singular kernel are analyzed.
T. Diogo, P. Lima
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A family of singular ordinary differential equations of the third order with an integral boundary condition

Boundary Value Problems, 2018
We establish in this paper the equivalence between a Volterra integral equation of the second kind and a singular ordinary differential equation of the third order with two initial conditions and an integral boundary condition, with a real parameter ...
Mahdi Boukrouche, Domingo A. Tarzia
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