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The performance index of an FFOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a set of Fuzzy Fractional Differential Equations (FFDEs). After obtaining Euler\u2013Lagrange equations for FFOCPs and the necessary and sufficient conditions for the existence of solutions, using the definition of generalized Hukuhara differentiability (types I, II), the problem is considered in two cases. Then the distance function and an approach similar to the variational type along with the Lagrange multiplier method are used to formulate and solve the equations in a system. Time-invariant and time-varying examples are provided to assess the presented method. Numerical results show a similar trend for the state and control variables for various numbers of Legendre polynomials. Also, the convergence of state and control variables for the time-invariant system can be seen, and the same is true for control variables for the time-varying system.<\/jats:p>","DOI":"10.3233\/jifs-210583","type":"journal-article","created":{"date-parts":[[2022,1,21]],"date-time":"2022-01-21T11:39:39Z","timestamp":1642765179000},"page":"3827-3858","source":"Crossref","is-referenced-by-count":2,"title":["A numerical method for approximating the solution of fuzzy fractional optimal control problems in caputo sense using legendre functions"],"prefix":"10.1177","volume":"43","author":[{"given":"M.","family":"Mirvakili","sequence":"first","affiliation":[{"name":"Department of Mathematics, Payame Noor University (PNU), Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"Allahviranloo","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"Soltanian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Payame Noor University (PNU), Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"issue":"3","key":"10.3233\/JIFS-210583_ref1","first-page":"287","article-title":"An Efcient Numerical Scheme for SolvingFractional Optimal Control Problems","volume":"14","author":"Khader","year":"2012","journal-title":"International Journal ofNonlinear Science"},{"key":"10.3233\/JIFS-210583_ref3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.cam.2017.09.039","article-title":"Asurvey on fuzzy fractional differential and optimal control nonlocalevolution equations","volume":"339","author":"Agarwal","year":"2018","journal-title":"Journal of Computational and AppliedMathematics"},{"key":"10.3233\/JIFS-210583_ref4","first-page":"106","article-title":"A new fractional orthogonal basis and its applicationin nonlinear delay fractional optimal control problems","volume":"114","author":"Marzban","year":"2021","journal-title":"ISATransactions"},{"key":"10.3233\/JIFS-210583_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-0457-6"},{"key":"10.3233\/JIFS-210583_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14574-2"},{"key":"10.3233\/JIFS-210583_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14003-7"},{"key":"10.3233\/JIFS-210583_ref10","doi-asserted-by":"crossref","first-page":"1644","DOI":"10.1016\/j.camwa.2009.08.006","article-title":"An approximate method for numericallysolving fractional order optimal control problems of general form","volume":"59","author":"Tricaud","year":"2010","journal-title":"Computers and Mathematics with Applications"},{"key":"10.3233\/JIFS-210583_ref13","doi-asserted-by":"crossref","first-page":"2677","DOI":"10.1016\/j.na.2007.08.042","article-title":"Basic theory of fractionaldifferential equations","volume":"69","author":"Lakshmikantham","year":"2008","journal-title":"Nonlinear Anal"},{"key":"10.3233\/JIFS-210583_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.11.029"},{"issue":"2","key":"10.3233\/JIFS-210583_ref15","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/BF02083817","article-title":"Fractional-order diffusion-wave equation","volume":"35","author":"El-Sayed","year":"1996","journal-title":"Internat. 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