A New Optimization Method Based on Generalized Polynomials for Fractional Differential Equations

• Autorzy: Hassani H. , Dahaghin M. S. , Heydari M. H. , Eshkaftaki A. B.

Identyfikatory

DOI

10.3233/FI-2017-1503

• Języki publikacji: EN

Abstrakty

EN

In this paper, we present a new optimization method based on a new class of functions, namely generalized polynomials (GPs) for solving linear and nonlinear fractional differential equations (FDEs). In the proposed method, the solution of the problem under study is expanded in terms of the GPs with fixed coefficients, free coefficients and control parameters. The initial conditions are employed to compute the fixed coefficients. The residual function and its ǁ.ǁ2 are employed for converting the problem under consideration to an optimization one and then choosing the unknown free coefficients and control parameters optimally. As a useful result, the necessary conditions of optimality are derived as a system of nonlinear algebraic equations with unknown free coefficients and control parameters. The validity and accuracy of the approach are illustrated by some numerical examples. The obtained results show that the proposed method is very efficient and accurate.

Słowa kluczowe

EN

optimization method; generalized polynomials; GPs; free coefficients; fixed coefficients; control parameters; fractional differential equations; FDEs

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2017
• Tom: Vol. 151, nr 1/4
• Strony: 443--457
• Opis fizyczny: Bibliogr. 50 poz., tab., wykr.

Twórcy

autor

Hassani H.

• Department of Mathematics, Shahrekord University, Shahrekord, Iran

autor

Dahaghin M. S.

• Department of Mathematics, Shahrekord University, Shahrekord, Iran

autor

Heydari M. H.

• Department of Mathematics, Fasa University, Fasa, Iran

autor

Eshkaftaki A. B.

• Department of Mathematics, Shahrekord University, Shahrekord, Iran

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