In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...

There are several classifications of linear Integral Equations. Some them include; Voltera Equations, Fredholm Linear Fredholm-Voltera Integrodifferential. In the past, solutions higher-order Fredholm-Volterra Integrodifferential Equations [FVIE] have been presented. However, this work uses a computational techniques premised on third kind Chebyshev polynomials method. The performance results f...

In this paper, we study the global existence of solutions for the initial value problems for Volterra-Fredholm type neutral impulsive functional integrodifferential equations. Using the Leray-Schauder’s Alternative theorem, we derive conditions under which a solution exists globally. An application is provided to illustrate the theory.

We aim to study the convergence of the homotopy analysis method (HAM in short) for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exac...

In this note, convex Homotopy perturbation method (HPM) is presented for the approximate solution of the linear Fredholm-Volterra integral and integro-differential equation. Convergence and rate of convergence of the HPM are proved for both equations. Five numerical examples are provided to verify the validity and accuracy of the proposed method. Example reveals that HPM is very accurate and si...

In this paper, the successive overrelaxation iteration and the variation of parameters formula are used to discuss the stability of linear and nonlinear Volterra integrodifferential equations. Some sufficient conditions are obtained, such that the trivial solution of the Volterra integrodifferential equations is asymptotically stable; these stability conditions are given directly from the coeff...

In this paper the method of integral equations is proposed for some problems of electrical engineering ( current density, radiative heat transfer, heat conduction). Presented models lead to a system of Fredholm integral equations, integro-differential equations or Volterra-Fredholm integral equations, respectively. We propose various numerical methods (discretization method and projection metho...

in this article the nonlinear mixed volterra-fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (m3d-bfs). this method converts the nonlinear mixed volterra-fredholm integral equations into a nonlinear system of algebraic equations. the illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.