This paper deals with a recent approximate analytical approach of the
multistage optimal homotopy asymptotic method (MOHAM) for fractional optimal
control problems (FOCPs). In this paper, FOCPs are developed in terms of a
conformable derivative operator (CDO) sense. It is validated that the right CDO
appears naturally in the formulation even when the system dynamics are described
with the left CDO only. The CDO is employed to enlarge the stability region of the
dynamical systems of the optimal control problems (OCPs). The necessary and
transversal conditions are achieved using a Hamiltonian technique. The results
demonstrated that as the fractional-order solution derivative tends to integer-order 1,
the formulations lead to integer-order system solutions. Numerical results and a
comparison with the exact solution and other approximate analytical solutions in
fractional order are given to validate the efficiency of the MOHAM. Some numerical
examples are included to demonstrate the effectiveness and applicability of the new
technique.
Keywords: Approximate analytical solution, Convergence analysis, Conformable derivative operator, Fractional calculus, Fractional Hamiltonian approach, Fractional optimal control problems.
