  We introduce a numerical method, based on modified hat functions, for solving
a class of fractional optimal control problems. In our scheme, the control and
the fractional derivative of the state function are considered as linear
combinations of the modified hat functions. The fractional derivative is
considered in the Caputo sense while the Riemann-Liouville integral operator is
used to give approximations for the state function and some of its derivatives.
To this aim, we use the fractional order integration operational matrix of the
modified hat functions and some properties of the Caputo derivative and
Riemann-Liouville integral operators. Using results of the considered basis
functions, solving the fractional optimal control problem is reduced to the
solution of a system of nonlinear algebraic equations. An error bound is proved
for the approximate optimal value of the performance index obtained by the
proposed method. The method is then generalized for solving a class of
fractional optimal control problems with inequality constraints. The most
important advantages of our method are easy implementation, simple operations,
and elimination of numerical integration. Some illustrative examples are
considered to demonstrate the effectiveness and accuracy of the proposed
technique.
