Application of Transcendental Bernstein Polynomials for Solving Two-Dimensional Fractional Optimal Control Problems

Abstract

The aim of this study is to introduce a novel method to solve a class of two-dimensional fractional optimal control problems. Since there are some difficulties solving these problems using analytical methods, thus finding numerical methods to approximate their solution is a challenging topic. In this study, we use transcendental Bernstein series. In fact, for solving the problem, we generalize the Bernstein polynomials to a larger class of functions which can provide more accurate approximate solutions. The convergence theorem is proved. Some examples are solved to demonstrate the validity and applicability of this technique. Comparing the results with other methods, we can find the efficiency and applicability of the scheme.