An indirect spectral shifted Gegenbauer collocation method for discretizing fractional optimal control problems

Many best properties of the shifted Gegenbauer functions were used to obtain a new closed formula of the left and right Riemann-Liouville fractional derivative.The new formulas have been used to approximate the solution of the fractional optimal control problems (FOCPs).The indirect spectral-shifted Gegenbauer collocation method is applied to discretizing FOCPs with a dynamic fractional differential equation.The FOCPs were reduced to the system of algebraic equations.Special attention is given to studying the convergence analysis and estimating an error upper bound of the presented formulas.Illustrative numerical examples are integrated to show the truth and applicability of this new technique.