Khanduzi, RahelehBeik, Samaneh P. A.Baleanu, DumitruEbrahimzadeh, Asiyeh2022-12-152025-09-182022-12-152025-09-182023Ebrahimzadeh, Asiyeh...et al. (2021). "Research on a collocation approach and three metaheuristic techniques based on MVO, MFO, and WOA for optimal control of fractional differential equation", JVC/Journal of Vibration and Control.1077-54631741-2986https://doi.org/10.1177/10775463211051447https://hdl.handle.net/20.500.12416/11077Khanduzi, Raheleh/0000-0002-0979-4041; Ebrahimzadeh, Asiyeh/0000-0002-4684-7640Exploiting a comprehensive mathematical model for a class of systems governed by fractional optimal control problems is the significant focal point of the current paper. The efficiency index is a function of both control and state variables and the dynamic control system relies on Caputo fractional derivatives. The attributes of Bernoulli polynomials and their operational matrices of fractional Riemann-Liouville integrations are applied to convert the optimization problem to the nonlinear programing problem. Executing multi-verse optimizer, moth-flame optimization, and whale optimization algorithm terminate to the most excellent solution of fractional optimal control problems. A study on the advantage and performance between these approaches is analyzed by some examples. Comprehensive analysis ascertains that moth-flame optimization significantly solves the example. Furthermore, the privilege and advantage of preference with its accuracy are numerically indicated. Finally, results demonstrate that the objective function value gained by moth-flame optimization in comparison with other algorithms effectively decreased.eninfo:eu-repo/semantics/closedAccessOptimal ControlFractional Differential EquationBernoulli PolynomialsMoth-Flame OptimizationMulti-Verse OptimizerWhale Optimization AlgorithmArticle10.1177/107754632110514472-s2.0-85120570036