in recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. these two tools that mathematicians have developed, differential equations and optimal control theory, are probably the most basic for economists to analyze dynamic problems. in this paper i will consider the linear differential equations on the plane (phase diagram) and elements of nonl...

In this paper, a numerical procedure for solving a class of nonlinear VolterraFredholm integral equations is presented. The method is based upon the globally defined sinc basis functions. Properties of the sinc procedure are utilized to reduce the computation of the nonlinear integral equations to some algebraic equations. Illustrative examples are included to demonstrate the validity and appli...

Abstract The functional equations, functional integral equations and functional differential equations have many applications in nonlinear analysis. Also, the fractional order integral equations and fractional order differential equations have many applications in mathematical physics. Here we study the existence of solutions of a functional integral equations of arbitrary (fractional) order in...

We study discrete solutions of nonlinear optimal control problems. By value functions , we construct difference equations to approximate the optimal control on each interval of " small " time. We aim to find a discrete optimal feedback control. An algorithm is proposed for computing the solution of the optimal control problem. 1. Introduction and statement of the problem. For nonlinear analytic...

The integral inequalities occupy privileged position in the theory of differential and integral equations. In the recent years nonlinear integral inequalities have received considerable attention because of their important applications to a variety of problems in diverse fields of nonlinear differential and integral equations. In 1919, Gronwall [4] introduced the famous Gronwall inequality in t...