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By means of collocation points the introduced method converts the proposed problem to solving a system of algebraic equations with shifted Chebyshev coefficients.
Laplace and Fourier integral transforms are used to reduce the transient problem to solving a singular integral equation with a generalized Cauchy kernel in the Laplace transform domain.
An important moment of our research is fact that using a Carleman-Vekua regularization method [4], we reduce the initial problem to solving the Abel integral equation of the second kind.
In the proposed method, the structural modification is considered as an inverse eigenvalue problem and calculated eigenderivatives are used for transforming this inverse problem to solving a system of algebraic equations.
The method reduces the problem to solving from two to four real-valued generalized linear fractional programs, which can be computed in polynomial time using an appropriate interior point method solver.
And in [7], Bhrawy et al. used the Rayleigh-Ritz method for the necessary conditions of optimization and the operational matrix of fractional derivatives together with the help of the properties of the shifted Legendre orthonormal polynomials to reduce the fractional optimal control problem to solving a system of algebraic equations that greatly simplifies the problem.
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Justyna Jupowicz-Kozak
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