Nemati, S. (2016). A spectral method based on the second kind Chebyshev polynomials for solving a class of fractional optimal control problems. Sahand Communications in Mathematical Analysis, 04(1), 15-27.

Somayeh Nemati. "A spectral method based on the second kind Chebyshev polynomials for solving a class of fractional optimal control problems". Sahand Communications in Mathematical Analysis, 04, 1, 2016, 15-27.

Nemati, S. (2016). 'A spectral method based on the second kind Chebyshev polynomials for solving a class of fractional optimal control problems', Sahand Communications in Mathematical Analysis, 04(1), pp. 15-27.

Nemati, S. A spectral method based on the second kind Chebyshev polynomials for solving a class of fractional optimal control problems. Sahand Communications in Mathematical Analysis, 2016; 04(1): 15-27.

A spectral method based on the second kind Chebyshev polynomials for solving a class of fractional optimal control problems

^{}Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.

Abstract

In this paper, we consider the second-kind Chebyshev polynomials (SKCPs) for the numerical solution of the fractional optimal control problems (FOCPs). Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature formula to reduce the fractional optimal control problem to solving a system of nonlinear algebraic equations that greatly simplifies the problem. Finally, some examples are included to confirm the efficiency and accuracy of the proposed method.

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