Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨q)-fuzzy ideals, (∈,∈ ∨q)-fuzzy bi-ideals and (∈,∈ ∨q)-fuzzy generalized bi-ideals of an ordered semigroup S, and investigate their related properties. Furthermore, we also define the upper and lower parts of fuzzy subsets of an ordered semigroup S, and investigate the properties of (∈,∈ ∨q)-fuzzy ideals of S....

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...

The paper studies the finite-time blow-up theory for a class of nonlinear Volterra integro-differential equations. The conditions for the occurrence of finite-time blow-up for nonlinear Volterra integro-differential equations are provided. Moreover, the finite-time blow-up theory for nonlinear partial Volterra integro-differential equations with general kernels is also established using the blo...

We study a dynamic model for viscoelastic materials based on a constitutive equation of fractional order. This results in an integrodifferential equation with a weakly singular convolution kernel. We discretize in the spatial variable by a standard Galerkin finite element method. We prove stability and regularity estimates which show how the convolution term introduces dissipation into the equa...

In the present article, we implement the new iterative method with a reliable algorithm to solve the nth-order linear/ nonlinear integro-differential equations. The obtained results confirm the power of the method in reducing the size of calculations compared with the other methods.

In this paper we discuss the numerical solution of initial-boundary value problem for the fourth order parabolic partial integro-differential equation. We use the forward Euler scheme for time discretization and the quasi-wavelet method for space discretization. Sometimes, we give a new method about the treatment of boundary condition. Numerical experiment is included to demonstrate the validit...

In the present article we study the stabilization of first-order linear integro-differential hyperbolic equations. For such equations we prove that the stabilization in finite time is equivalent to the exact controllability property. The proof relies on a Fredholm transformation that maps the original system into a finite-time stable target system. The controllability assumption is used to prov...

1Department of Mathematics, Alzahra University, Tehran, Iran 2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-51167, Iran (Received November07, 2011, accepted March 1, 2012) Abstract. The sinc-collocation method is presented for solving second-order boundary value problems of nonlinear integro-differential equation. The method is effective...

In this paper, we prove the existence of at least three positive solutions of boundary value problems for nth order nonlinear impulsive integrodifferential equations of mixed type on infinite interval with infinite number of impulsive times. Our results are obtained by applying a new fixed point theorem introduced by Avery and Peterson.

* Correspondence: [email protected] Department of Mathematics and Computer Sciences, Cankaya University, Eskisehir Yolu 29. km, YukariYurtcu Mah. No 80, 06810 Yenimahalle, Ankara, Turkey Full list of author information is available at the end of the article Abstract Our aim in this work is to study the existence and the attractivity of solutions for a system of delay partial integro-differ...