@article { author = {shafiof, seyed mehdy and Askari, Javad and Shams Solary, Maryam}, title = {A Numerical Solution of Fractional Optimal Control Problems Using Spectral Method and Hybrid Functions}, journal = {Control and Optimization in Applied Mathematics}, volume = {3}, number = {1}, pages = {1-25}, year = {2018}, publisher = {Payame Noor University (PNU)}, issn = {2383-3130}, eissn = {2538-5615}, doi = {10.30473/coam.2019.46969.1119}, abstract = {In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based on the spectral Ritz method‎. ‎Also‎, ‎two new methods are proposed for calculating the left Caputo fractional derivative and right Riemann-Liouville fractional derivative operators of the hybrid functions that are proportional to the Ritz method‎. ‎The FOCP is converted into a system of the algebraic equations by applying the fractional derivative operators and collocation method‎, ‎which determines the solution of the problem‎. ‎Error estimates for the hybrid function approximation‎, ‎fractional operators and‎, ‎the proposed method are provided‎. ‎Finally‎, ‎the efficiency of the proposed method and its accuracy in obtaining optimal solutions are shown by some test problems.}, keywords = {Fractional optimal control‎,‎Hybrid functions‎,‎Bernoulli polynomials‎,‎Ritz method‎,‎Error bound}, url = {https://mathco.journals.pnu.ac.ir/article_6287.html}, eprint = {https://mathco.journals.pnu.ac.ir/article_6287_704ba4697435e956e25090929183272c.pdf} }