A numerical technique for solving fractional optimal control problems and fractional Riccati differential equations

In the present paper, we apply the Bezier curves method for solving fractional optimal control problems (OCPs) and fractional Riccati differential equations. The main advantage of this method is that it can reduce the error of the approximate solutions. Hence, the solutions obtained using the Bezier curve method give good approximations. Some numerical examples are provided to confirm the accuracy of the proposed method. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13

A new approach for solving fractional differential-algebraic equations

In this paper, the Bezier curves method is implemented to give approximate solutions for fractional differential-algebraic equations (FDAEs). This methods in applied mathematics can be used as approximated method for obtaining approximate solutions for different types of fractional differential equations. An illustrative example is included to demonstrate the validity and applicability of the suggested approach. Keywords: Fractional differential-algebraic equations (FDAEs), Numerical solution, Bezier metho

Bezier Curves for Solving Fredholm Integral Equations of the Second Kind

The Bezier curves are presented to estimate the solution of the linear Fredholm integral equation of the second kind. A direct algorithm for solving this problem is given. We have chosen the Bezier curves as piecewise polynomials of degree n and determine Bezier curves on [0, 1] by n+1 control points. Numerical examples illustrate that the algorithm is applicable and very easy to use

Bezier Curves Method for Fourth-Order Integrodifferential Equations

The Bezier curves method is applied to solve both linear and nonlinear BVPs for fourth-order integrodifferential equations. Also, the presented method is developed for solving BVPs which arise from the problems in calculus of variation. These BVPs result from the Euler-Lagrange equations which are the necessary conditions of the extremums of problems in calculus of variation. Some numerical examples demonstrate the validity and applicability of the technique

Bezier Curves Based Numerical Solutions of Delay Systems with Inverse Time

This paper applied, for the first time, the Bernstein’s approximation on delay differential equations and delay systems with inverse delay that models these problems. The direct algorithm is given for solving this problem. The delay function and inverse time function are expanded by the Bézier curves. The Bézier curves are chosen as piecewise polynomials of degree n, and the Bézier curves are determined on any subinterval by n+1 control points. The approximated solution of delay systems containing inverse time is derived. To validate accuracy of the present algorithm, some examples are solved