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چکیده
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his manuscript examines two categories of fractional optimal control problems (FOCPs) with fractional system and delay fractional system constraints. This scheme is based on the general Lagrange scaling functions (GLSFs), which can generate both orthogonal and non-orthogonal scaling functions by selecting different Lagrange nodes. Notably, the method is designed to be applied without initially choosing specific Lagrange nodes; instead, we leverage the potential advantages of GLSFs to develop new methods by considering various Lagrange nodes. Additionally, a general Riemann-Liouville fractional integration operational matrix (GR-LOP) and a general delay operational matrix (GDOP) are proposed for the considered functions. Next, by combining these operational matrices and the Gauss-Legendre integration method, we transform the original problems into systems of algebraic equations. To demonstrate the effectiveness of the proposed GLSF method, five numerical examples are provided.
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