In this paper the solution of the Volterra integro-differential equations of fractional order is presented. The proposed method consists in constructing the functional series, sum of which determines the function giving the solution of considered problem. We derive conditions under which the solution series, constructed by the method is convergent. Some examples are presented to verify convergen...

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...

In this work, the existence and uniqueness solution of fractional nonlinear mixed integro-differential equation (FrNMIoDE) is guaranteed with a general discontinuous kernel based on position time-space L2Ω×C0,T, T<1. The FrNMIoDE conformed to Volterra-Hammerstein integral (V-HIE) second kind, after applying characteristics integral, in for Hammerstein term continuous time Volterra (VI) term....

Bu çalışmada, singüler pertürbe Volterra integro-diferansiyel denklemlerin yaklaşık çözümü için nümerik integrasyon yöntemi uygulanır. İlk olarak düzgün bir şebeke üzerinde sonlu fark metodu ile başlanır daha sonra integraller trapez kullanılır. Buradan elde edilen denklem sistemi Thomas algoritması çözülür. Önerilen yöntemin doğruluğunu ve ekonomikliğini ortaya koyan örnek sunulur.

This article presents a numerical method for solving nonlinear two-dimensional fractional Volterra integral equation. We derive the Hat basis functions operational matrix of order integration and use it to solve integro-di?erential equations. The is described illustrated with examples. Also, we give error analysis.

We consider a variable-structure optimal control problem described in different domains by hyperbolic integro-differential equation and Volterra integral equation, respectively. The quality functional is terminal. A formula for the increment of criterion constructed an analogue L.S. Pontryagin's maximum principle proved investigating on special McShane-type variations.

We discuss a possibility to construct high order methods on uniform or mildly graded grids for the numerical solution of linear Volterra integro-differential equations with weakly singular or other nonsmooth kernels. Using an integral equation reformulation of the initial value problem, we apply to it a smoothing transformation so that the exact solution of the resulting equation does not conta...