Results 71 to 80 of about 2,313,393 (156)

A Multiple Iterated Integral Inequality and Applications

Journal of Applied Mathematics, 2014
We establish new multiple iterated Volterra-Fredholm type integral inequalities, where the composite function w(u(s)) of the unknown function u with nonlinear function w in integral functions in [Ma, QH, Pečarić, J: Estimates on solutions of some new ...
Zongyi Hou, Wu-Sheng Wang
doaj   +1 more source

Existence and Uniqueness of Solutions to Initial Value Problems of High‐Order Fractional Fuzzy Differential Equations

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
High‐order fractional fuzzy differential equations show great potential in modeling complex systems with memory effects and uncertainty. Existing qualitative theories seldom involve both Caputo‐type strongly generalized Hukuhara differentiability and coupled integral operators on infinite intervals. This paper presents a systematic investigation of the
Yanli Xi, Wenbin Bao, Mohammad Rezwan Habib   +2 more
wiley   +1 more source

Integral equations for the wave function of particle systems

Semiconductor Physics, Quantum Electronics & Optoelectronics, 2019
Constructions of integral equations to the wave function of particle systems in bound state have been proposed in this work. We obtain the kernel of the Fredholm type integral equation for an odd number of particles in explicit form. Besides, an integral
K.V. Avdonin
doaj   +1 more source

Convergence Analysis of the Tau Method for Volterra–Fredholm Integrodifferential Equations With Weakly Singular Kernel

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This work focuses on the analysis of the Volterra–Fredholm integral equation (VFIE) with a weakly singular kernel, which is a transformed form of a partial integrodifferential equation (PIDE) with a weakly singular kernel. We present an approach based on the spectral Tau method for determining the unknown function in the VFIE formulation with respect ...
Javad Shokri, Saeed Pishbin, Ahmed M. Rajab, Youssri Hassan Youssri   +3 more
wiley   +1 more source

Block-by-Block Method for Solving Nonlinear Volterra-Fredholm Integral Equation [PDF]

, 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.
Abdallah A. Badr
core   +1 more source

Numerical method for the mixed Volterra-Fredholm integral equations using hybrid Legendre functions [PDF]

, 2015
summary:A new method is proposed for the numerical solution of linear mixed Volterra-Fredholm integral equations in one space variable. The proposed numerical algorithm combines the trapezoidal rule, for the integration in time, with piecewise ...
Lima, P., Ordokhani, Y., Nemati, S.
core   +1 more source

Numerical Study of Fourth‐Order Volterra Partial Integrodifferential Equation With Weakly Singular Kernel via Subdivision Collocation Approach

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In the present article, an emerging subdivision‐based technique is developed for the numerical solution of linear Volterra partial integrodifferential equations (LVPIDEs) of order four with a weakly singular kernel. To approximate the spatial derivatives, the basis function of the subdivision scheme is used, whereas the time discretization is done with
Zainab Iqbal, Syeda Tehmina Ejaz, Jihad Younis, M. I. Elashiry, Faizah D. Alanazi, Nikhil Khanna   +5 more
wiley   +1 more source

Existence and Stability Theorems for Implicit Neutral Fractional Integrodifferential Equations With Computational Results

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
This paper investigates a class of nonlinear implicit neutral integrodifferential equations involving Hilfer–Katugampola fractional operators, which provide an effective framework for describing dynamical systems with memory and hereditary properties. By converting the considered problem into an equivalent fractional integral equation, we show that the
Manal Elzain Mohamed Abdalla, Hasanen A. Hammad, Tarek Aboelenen, Mohammed S. Abdo   +3 more
wiley   +1 more source

Efficient numerical methods for Volterra integral equations of Hammerstein type [PDF]

, 2006
Volterra integral equations (VIEs) are the mathematical model of many evolutionary problems with memory arising from biology, chemistry, physics, engineering.
Del Prete, Ida
core   +1 more source

On the Stability of Fractional Integro‐Differential Equations of Ψ‐Hilfer Type

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In this article, we investigate some properties such as the existence, uniqueness, and Ulam–Hyers–Rassias stability for the fractional Volterra–Fredholm integrodifferential equations of Ψ‐Hilfer type with boundary conditions. We prove the desired results by using the Banach fixed point theorem and the Schauder fixed point theorem.
Malayin A. Mohammed, Sahar M. A. Maqbol, Ram G. Metkar, Udhayakumar Ramalingam   +3 more
wiley   +1 more source