Defterli, Ozlem2016-06-152025-09-182016-06-152025-09-182010Defterli, Ö. (2010). A numerical scheme for two dimensional optimal control problems with memory effect.Computers&Mathematics With Applications, 59(8), 1630-1636. http://dx.doi.org/10.1016/j.camwa.2010.03.0010898-12211873-7668https://doi.org/10.1016/j.camwa.2009.08.005https://hdl.handle.net/20.500.12416/14010A new formulation for multi-dimensional fractional optimal control problems is presented in this article. The fractional derivatives which are coming from the formulation of the problem are defined in the Riemann-Liouville sense. Some terminal conditions are imposed on the state and control variables whose dimensions need not be the same. A numerical scheme is described by using the Grunwald-Letnikov definition to approximate the Riemann-Liouville Fractional Derivatives. The set of fractional differential equations, which are obtained after the discretization of the time domain, are solved within the Grunwald-Letnikov approximation to obtain the state and the control variable numerically. A two-dimensional fractional optimal control problem is studied as an example to demonstrate the performance of the scheme. (C) 2009 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/openAccessFractional CalculusFractional HamiltonianVariational AnalysisOptimal ControlQuadratic Performance IndicesArticle10.1016/j.camwa.2009.08.0052-s2.0-76449103001