The initial-value problem for a class of Volterra functional differential equations— of sufficient generality to encompass, as special cases, ordinary differential equations, retarded differential equations, integro-differential equations, and hysteretic differential equations— is studied. A self-contained and elementary treatment of this over-arching problem is provided, in which a unifying th...

The fuzzy set theory introduced by Zadeh has emerged as an interesting and fascinating branch of pure and applied sciences. The applications of fuzzy set theory can be found in many branches of regional, physical, mathematical, differential equations andengineering sciences. Recently, the authors have made important research results in the theory of fuzzy differentialequations, integrodifferent...

In this paper, operational matrix method based upon the Bernstein polynomials is proposed to solve the variable order fractional integro-differential equations in the Caputo derivative sense. We derive the Bernstein polynomials operational matrix of fractional order integration and introduce the product operational matrix of Bernstein polynomials. A truncated the Bernstein polynomials series to...

in this paper, a  fuzzy numerical procedure for solving fuzzy linear volterra integro-differential equations of the second kind under strong  generalized differentiability is designed. unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method  and other numerical methods.error ana...

In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the nonlinear integro-differential equation , , , where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are sol...

In this paper, we use parametric form of fuzzy number, then aniterative approach for obtaining approximate solution for a classof nonlinear fuzzy Fredholmintegro-differential equation of the second kindis proposed. This paper presents a method based on Newton-Cotesmethods with positive coefficient. Then we obtain approximatesolution of the nonlinear fuzzy integro-differential equations by an it...

Linear quasi-parabolic integro-differential equations and their control appear in many scientific problems and engineering applications such as biology mechanics, nuclear reaction dynamics, heat conduction in materials with memory, and visco-elasticity, etc.. The existence and uniqueness of the solution of the linear quasi-parabolic integro-differential equations have been studied by Wheeler M....

An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations ...

The objective of this paper is to analyse the application of the Half-Sweep Gauss-Seidel (HSGS) method by using the Half-sweep approximation equation based on central difference (CD) and repeated trapezoidal (RT) formulas to solve linear fredholm integro-differential equations of first order. The formulation and implementation of the Full-Sweep Gauss-Seidel (FSGS) and HalfSweep Gauss-Seidel (HS...