In this paper, we study the dividend payments prior to absolute ruin in a Markov-dependent risk process in which the claim occurrence and the claim amount are regulated by an external discrete time Markov chain. A system of integrodifferential equations with boundary conditions satisfied by the moment-generating function, the nth moment of the discounted dividend payments prior to absolute ruin...

Fractional diffusions arise in the study of models from population dynamics. In this paper, we derive a class of integro-differential reactiondiffusion equations from simple principles. We then prove an approximation result for the first eigenvalue of linear integro-differential operators of the fractional diffusion type, and we study from that the dynamics of a population in a fragmented envir...

In this paper we propose the iterated projection method for the approximate solution of an integro-differential equations with Cauchy kernel in L2([−1, 1],C) using Legendre polynomials. We prove the convergence of the method. A system of linear equations is to be solved. Numerical examples illustrate the theoretical results. AMS Mathematics Subject Classification : 45E05, 35J15.

In this paper, the variational iteration method for solving nth-order fuzzy integro-differential equations (nth-FIDE) is proposed. In fact the problem is changed to the system of ordinary fuzzy integrodifferential equations and then fuzzy solution of nth-FIDE is obtained. Some examples show the efficiency of the proposed method.

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...

In this paper, a numerical method is proposed to solve FredholmVolterra fractional integro-differential equation with nonlocal boundary conditions. For this purpose, the Chebyshev wavelets of second kind are used in collocation method. It reduces the given fractional integro-differential equation (FIDE) with nonlocal boundary conditions in a linear system of equations which one can solve easily...

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...

This paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. Then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. Finally an example is given to illustrate the performance of the methods.

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...