Abstract
In the current study, a general formulation of the discrete Chebyshev polynomials is given. The operational matrix of fractional integration for these discrete polynomials is also derived. Then, a numerical scheme based on the discrete Chebyshev polynomials and their operational matrix has been developed to solve fractional variational problems. In this method, the need for using Lagrange multiplier during the solution procedure is eliminated. The performance of the proposed scheme is validated through some illustrative examples. Moreover, the obtained numerical results were compared to the previously acquired results by the classical Chebyshev polynomials. Finally, a comparison for the required CPU time is presented, which indicates more efficiency and less complexity of the proposed method.
Highlights
In the last two decades, numerical approaches based on orthogonal polynomials have been frequently used to approximate solution of fractional differential and integral equations [1, 5, 4, 3, 2]
The discrete Chebyshev polynomials belong to a rich family of orthogonal polynomials which introduced by Chebyshev
This paper proposed a new type of discrete orthogonal polynomials basis
Summary
In the last two decades, numerical approaches based on orthogonal polynomials have been frequently used to approximate solution of fractional differential and integral equations [1, 5, 4, 3, 2]. Continuous orthogonal polynomials have been more frequently used to approximate solution of functional equations, there are some advantages of using discrete orthogonal polynomials. The main purpose of this paper is to present a comparitive study of numerical solution of the following fractional variational problems:.
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