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چکیده
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This paper considers a type of fractional optimal control problem (FOCP) that we solve using an approximate technique based on fractional shifted Vieta-Fibonacci functions (FSV-FFs). For this purpose, we introduce FSV-FFs and some of their properties for the first time. Then the steps for constructing the operational matrix of the fractional integral of FSVFFs are illustrated. In addition, in the dynamic system, a derivative of the Caputo type is considered. The fractional integral operational matrix and the Gaussian quadrature formula are used to transfer the FOCP to an algebraic equation system, which is solved by Newton’s iterative method. In addition, we present an error bound for our approximation. Error analysis shows that the proposed method is convergent, and when the number of basis functions increases, the error quickly approaches zero. While a small number of FSV-FFs are utilized to obtain a satisfactory result, the necessary time for computation is shortened. Finally, to confirm the accuracy and effectiveness of the method, some illustrative tests are examined.
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