El-Kalaawy, A. A.Doha, E. H.Ezz-Eldien, S. S.Abdelkawy, M. A.Hafez, R. M.Amin, A. Z. M.Baleanu, D.Zaky, M. A.2019-11-092019-11-092018EDITURA ACAD ROMANE, CALEA 13 SEPTEMBRIE NR 13, SECTOR 5, BUCURESTI 050711, ROMANIA1221-1451https://cutt.ly/WeUjgfpAccession Number: WOS:000438016900005This paper is devoted to investigate, from the numerical point of view, fractional-order Gegenbauer functions to solve fractional variational problems and fractional optimal control problems. We first introduce an orthonormal system of fractional-order Gegenbauer functions. Then, a formulation for the fractional-order Gegenbauer operational matrix of fractional integration is constructed. An error upper bound for the operational matrix of the fractional integration is also given. The properties of the fractional-order Gegenbauer functions are utilized to reduce the given optimization problems to systems of algebraic equations. Some numerical examples are included to demonstrate the efficiency and the accuracy of the proposed approach.enUniversity for Fractional variational problemsFractional optimal control problemsFractional-order Gegenbauer functionsOPERATIONAL MATRIXDIFFERENTIAL-EQUATIONSNUMERICAL TECHNIQUECONSERVATION-LAWSFORMULATIONAPPROXIMATIONCALCULUSSCHEMEArticle