In this paper, a numerical solution for a system of linear Fredholm integro-differential equations by means of the sinc method is considered. This approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. The exponential convergence rate $O(e^{-k sqrt{N}})$ of the method is proved. The analytical results are illustrated with numerical examp...

High order integro-differential equations (IDE), especially nonlinear, are usually difficult to solve even for approximate solutions. In this paper, we give a high accurate compact finite difference method to efficiently solve integro-differential equations, including high order and nonlinear problems. By numerical experiments, we show that compact finite difference method of integro-differenti...

An analytic technique, the homotopy analysis method (HAM), is applied to obtain the approximate analytical solutions of fourth-order integro-differential equations. The homotopy analysis method (HAM) is one of the most effective method to obtain the exact and approximate solution and provides us with a new way to obtain series solutions of such problems. HAM contains the auxiliary parameter ħ, ...

in this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. utilizing the generalized characterization theorem. then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. here neural network is considered as a part of large eld called n...

‎Semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. The model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎Stability estimates are obtained for a slightly more general problem.‎ ‎These, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎

In this paper, we give sufficient conditions to guarantee exponential decay of solutions to zero of the time varying delay differential equation of first order. By using the Lyapunov-Krasovskii functional approach, we establish new results on the exponential decay of solutions, which include and improve some related results in the literature. of linear impulsive differential equations with dist...

Coarsening of solutions of the integro-differential equation

In this paper, we investigate the existence of solutions of some three-point boundary value problems for n-th order nonlinear fractional differential equations with higher boundary conditions by using a fixed point theorem on cones.

Introducing shift operators on time scales we construct the integro-dynamic equation corresponding to the convolution type Volterra differential and difference equations in particular cases T = R and T = Z. Extending the scope of time scale variant of Gronwall’s inequality we determine function bounds for the solutions of the integro dynamic equation.

Abstract In this article, first, we present an example of fuzzy normed space by means the Mittag-Leffler function. Next, extend concept to matrix valued and also introduce a class control functions stabilize nonlinear ϕ -Hadamard fractional Volterra integro-differential equation. sense, investigate Ulam–Hyers–Rassias stability for kind equations in Banach space. Finally, as application, using f...