Legendre wavelet collocation method for fractional optimal control problems with fractional Bolza cost

This paper exhibits a numerical method for solving general fractional optimal control problems involving a dynamical system described by a nonlinear Caputo fractional differential equation, associated with a fractional Bolza cost composed as the aggregate of a standard Mayer cost and a fractional Lagrange cost given by a Riemann-Liouville fractional integral. By using the Lagrange multiplier within the calculus of variations and by applying integration by part formula, the necessary optimality conditions are derived in terms of a nonlinear two-point fractional-order boundary value problem. An operational matrix of fractional order right Riemann-Liouville integration is proposed and by utilizing it, the obtained two-point fractional-order boundary value problem is reduced into the solution of an algebraic system. An L-2-error estimate in the approximation of unknown variable by Legendre wavelet is derived and in the last, illustrative examples are included to demonstrate the applicability of the proposed method.