Abstract The Laplace transform method is applied in this article to study the semi-Hyers-Ulam-Rassias stability of a Volterra integro-differential equation order n, with convolution-type kernel. This kind extends original Hyers-Ulam whose originated 1940. A general integral formulated first, and then some particular cases (polynomial function exponential function) for from kernel are considered.

The purpose of this study is to present an approximate numerical method for solving high order linear Fredholm-Volterra integro-differential equations in terms of rational Chebyshev functions under the mixed conditions. The method is based on the approximation by the truncated rational Chebyshev series. Finally, the effectiveness of the method is illustrated in several numerical examples. The p...

We study the numerical approximation of an integro-differential equation which is intermediate between the heat and wave equations. The proposed discretization uses convolution quadrature based on the firstand second-order backward difference methods in time, and piecewise linear finite elements in space. Optimal-order error bounds in terms of the initial data and the inhomogeneity are shown fo...

To solve the weakly-singular Volterra integro-differential equations, the combined method of the Laplace Transform Method and the Adomian Decomposition Method is used. As a result, series solutions of the equations are constructed. In order to explore the rapid decay of the equations, the pade approximation is used. The results present validity and great potential of the method as a powerful al...

We establish Pohozaev identities and integration by parts type formulas for anisotropic integro-differential operators of order 2s, with s ∈ (0, 1). These identities involve local boundary terms, in which the quantity u/d|∂Ω plays the role that ∂u/∂ν plays in the second order case. Here, u is any solution to Lu = f(x, u) in Ω, with u = 0 in R \ Ω, and d is the distance to ∂Ω.

This paper presents a computational technique for solving linear and nonlinear Fredholm integro-differential equations of fractional order. In addition, examples that illustrate the pertinent features of this method are presented, and the results of the study are discussed. Results have revealed that the RKHSM yields efficiently a good approximation to the exact solution.

We review some regularity results for integro-differential equations, focusing on Hölder estimates for equations with rough kernels and their applications. We show that if we take advantage of the integral form of the equation, we can obtain simpler proofs than for second order equations. For the equations considered here, the Harnack inequality may not hold. Mathematics Subject Classification ...

In this paper, the method of upper and lower solutions and monotone iterative technique are employed to the study of nonlinear three-point boundary value problems for a class of first order impulsive integro-differential equations of mixed type. Sufficient conditions for the existence of extreme solutions are obtained. Mathematics Subject Classification: 34B37

In the present paper, we investigate the existence, uniqueness and continuous dependence on initial data of mild solutions of first order nonlocal semilinear functional impulsive integro-differential equations of more general type with finite delay in Banach spaces. Our analysis is based on semigroup theory and Banach contraction theorem.