In this paper, the Ulam stability of an n-th order delay integro-differential equation is given. Firstly, existence and uniqueness theorem a solution for obtained using Lipschitz condition Banach contraction principle. Then, expression derived by mathematical induction. On basis, we obtain via Gronwall–Bellman inequality. Finally, two examples equations are given to explain our main results.

Abstract: The current paper is concerned with the controllability of nonlocal secondorder impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a ne...

The objective of this paper is to analyse the application of the Half-Sweep Gauss-Seidel (HSGS) method by using the Half-sweep approximation equation based on central difference (CD) and repeated trapezoidal (RT) formulas to solve linear fredholm integro-differential equations of first order. The formulation and implementation of the Full-Sweep Gauss-Seidel (FSGS) and HalfSweep Gauss-Seidel (HS...

We study a problem of optimal consumption and portfolio selection in a market where the logreturns of the uncertain assets are not necessarily normally distributed. The natural models then involve pure-jump L evy processes as driving noise instead of Brownian motion like in the Black and Scholes model. The state constrained optimization problem involves the notion of local substitution and is o...

The variational iteration method [1, 2], which is a modified general Lagrange multiplier method, has been shown to solve effectively, easily, and accurately a large class of nonlinear problems with approximations which converges (locally) to accurate solutions (if certain Lipschitz-continuity conditions are met). It was successfully applied to autonomous ordinary differential equations and nonl...