Constructing Efficient Bases From B-Spline Functions and Solving Fractional Optimal Control Problems

Abstract

In this article, we construct a new basis by twice integrating linear B-Spline functions. This new basis can expand functions similarly to linear B-Spline functions, but it also possesses the capability to exactly approximate third-order polynomials. We investigate the properties of these functions and apply them to solve fractional optimal control problems. By using this basis in the collocation method, the original problem is reduced to a nonlinear programming problem, enabling us to obtain approximate solutions through appropriate methods. The numerical results demonstrate the effectiveness of the new basis.