Using shifted Legendre orthonormal polynomials for solving fractional optimal control problems

‎‎shifted Legendre orthonormal polynomials (SLOPs) are used to approximate the numerical solutions of fractional optimal control problems‎. ‎To do so‎, ‎first‎, ‎the operational matrix of the Caputo fractional derivative‎, ‎the SLOPs‎, ‎and Lagrange multipliers are used to convert such problems into algebraic equations‎. ‎Also‎, ‎the method is proposed for solving multidimensional problems. ‎We obtained the error bound of the operational matrix in fractional derivatives and proved the convergence of the method‎. ‎Then‎, ‎this is tested on some nonlinear examples‎. ‎‎Comparison of our results with those obtained by other techniques in previous studies revealed the accuracy of the proposed technique for nonlinear and multidimensional problems‎.