this paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order volterra-fredholm integro-differential equation(vfides) and nonlinear fractional order integro-differential equations. our tools for this aims is operational matrices of integration and fractional integration. by this method the given problems reduce to solve a syst...

in this article, a numerical method based on  improvement of block-pulse functions (ibpfs) is discussed for solving the system of linear volterra and fredholm integral equations. by using ibpfs and their operational matrix of integration, such systems can be reduced to a linear system of algebraic equations. an efficient error estimation and associated theorems for the proposed method are also ...

In this research, the finite difference method is used to solve initial value problem of linear first order Volterra-Fredholm integro-differential equations with singularity. By using implicit rules and composite numerical quadrature rules, scheme established on a Shishkin mesh. The stability convergence proposed are analyzed two examples solved display advantages presented technique.

In this paper, we discuss several problems related to the neutral fractional Volterra-Fredholm integro-differential systems in Banach spaces. Existence of Schaefer's fixed point and Ulam-Hyers-Rassias stability properties for problem will be discussed. Some results are presented, under appropriate conditions, some open questions pointed out. Our extend recent given \(\psi\)-fractional derivative.

We develop a theoretical context in which to study the future-sequential regularization method developed by J. V. Beck for the Inverse Heat Conduction Problem. In the process, we generalize Beck’s ideas and view that method as one in a large class of regularization methods in which the solution of an ill-posed first-kind Volterra equation is seen to be the limit of a sequence of solutions of we...

The main idea proposed in this paper is the perturbed shifted Chebyshev Galerkin method for the solutions of delay Fredholm and Volterra integrodifferential equations. The application of the proposed method is also extended to the solutions of integro-differential difference equations. The method is validated using some selected problems from the literature. In all the problems that are considered...

The existence of Hilfer fractional stochastic Volterra–Fredholm integro-differential inclusions via almost sectorial operators is the topic our paper. researchers used calculus, analysis theory, and Bohnenblust–Karlin’s fixed point theorem for multivalued maps to support their findings. To begin with, we must establish a mild solution. In addition, show principle, an application presented.

I. Introductory Remarks. My main purpose in this paper is to prove a bifurcation theorem for nontrivial periodic solutions of a general system of Volterra integral equations. The motivation for considering this problem can be found in models which arise in population dynamics, epidemiology and economics [1,3,6], an example of which appears in §5. The approach taken is that which is usually refe...

First, we develop a direct operator method for solving boundary value problems class of nth order linear Volterra–Fredholm integro-differential equations convolution type. The proposed technique is based on the assumption that Volterra bijective and its inverse known in closed form. Existence uniqueness criteria are established exact solution derived. We then apply this to construct form fourth...

In this study, an effective technique upon compactly supported semi orthogonal cubic Bspline wavelets for solving nonlinear Volterra-Fredholm integral equations is proposed. Properties of B-spline wavelets and function approximation by them are first presented and the exponential convergence rate of the approximation, Ο(2 -4j ), is proved. For solving the nonlinear Volterra-Fredholm integral eq...