Abstract
In this current paper, we present a numerical method to solve a class of fractional optimal control problems of system described by integer-fractional derivative. The fractional derivative is explained in the Caputo sense and a new formulation for the Bernoulli Caputo fractional derivative operational matrix has been achieved for the first time. Then this matrix and operational matrix of multiplication of these polynomials are applied to solve the fractional-order optimal control problems by the direct method. As a matter of fact, the functions of the problem are approximated by Bernoulli polynomials with unknown coefficients in the functional and conditions. Therefore, a fractional optimal control problem is converted to an unconstrained optimization problem and then it could be solved via Newton’s iterative method. Also we demonstrate that if the number of Bernoulli basis is increased, this method is convergent. The effectiveness and validity of the new methodology are illustrated by four examples, in addition our findings in comparison with the existing results show the preference of presented method.
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