Numerical investigation of distributed-order fractional optimal control problems via Bernstein wavelets

The aim of this article is to investigate an efficient computational method for solving distributed-order fractional optimal control problems. In the proposed method, a new Riemann-Liouville fractional integral operator for the Bernstein wavelet is given. This approach is based on a combination of the Bernstein wavelets basis, fractional integral operator, Gauss-Legendre numerical integration, and Newton's method for solving obtained system. Easy implementation, simple operations, and accurate solutions are the essential features of the proposed method. The error analysis of the proposed method is carried out. Examples reveal the applicability of the proposed technique.

Automated summary

This article investigates an efficient computational method for solving distributed-order fractional optimal control problems. The method combines Bernstein wavelets basis, fractional integral operator, Gauss-Legendre numerical integration, and Newton's method, offering easy implementation, simple operations, and accurate solutions. Error analysis and examples demonstrate the applicability of the proposed technique.