Bhrawy, A. H.Doha, E. H.Tenreiro Machado, J. A.Ezz-Eldien, S. S.2019-11-202019-11-202015Cited References in Web of Science Core Collection: 371561-8625https://doi.org/10.1002/asjc.1109https://onlinelibrary.wiley.com/doi/full/10.1002/asjc.1109Accession Number: WOS:000363796100030The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.enUniversity for Fractional optimal control problemlegendre polynomialsoperational matrixlagrange multiplier methodcaputo derivativesriemann-liouville integralsArticlehttps://doi.org/10.1002/asjc.1109