A numerical approach for solving fractional optimal control problems with mittag-leffler kernel

In this work, we present a numerical approach based on the shifted Legendre polynomials for solving a class of fractional optimal control problems. The derivative is described in the Atangana-Baleanu derivative sense. To solve the problem, operational matrices of AB-fractional integration and multiplication, together with the Lagrange multiplier method for the constrained extremum, are considered. The method reduces the main problem to a system of nonlinear algebraic equations. In this framework by solving the obtained system, the approximate solution is calculated. An error estimate of the numerical solution is also proved for the approximate solution obtained by the proposed method. Finally, some illustrative examples are presented to demonstrate the accuracy and validity of the proposed scheme.

Automated summary

In this work, a numerical approach based on shifted Legendre polynomials is proposed for solving fractional optimal control problems, utilizing the Atangana-Baleanu derivative for the derivative operation. The method combines operational matrices of AB-fractional integration and multiplication with the Lagrange multiplier method to simplify the problem into a system of nonlinear algebraic equations, resulting in an approximate solution with proven error estimate. Illustrative examples are used to demonstrate the accuracy and validity of the proposed scheme.