  In [1], we inaugurated a new area of optimal control (OC) theory that we
called "periodic fractional OC theory," which was developed to find optimal
ways to periodically control a fractional dynamic system. The typical
mathematical formulation in this area includes the class of periodic fractional
OC problems (PFOCPs), which can be accurately solved numerically for a
fractional order {\alpha} in the range 0 < {\alpha} < 1 using Fourier
collocation at equally spaced nodes and Fourier and Gegenbauer quadratures. In
this study, we extend this earlier work to cover periodic higher-order
fractional OC problems (PHFOCPs) of any positive non-integer fractional order
{\alpha}.
