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Issue title: Theory and Applications of Fractional Fourier Transform and its Variants
Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han
Article type: Research Article
Authors: Hassani, Hosseina | Dahaghin, Mohammad Shafiea | Heydari, Mohammad Hosseinb; * | Eshkaftaki, Ali Bayatic
Affiliations: [a] Department of Mathematics, Shahrekord University, Shahrekord, Iran. [email protected], [email protected] | [b] Department of Mathematics, Fasa University, Fasa, Iran. [email protected] | [c] Department of Mathematics, Shahrekord University, Shahrekord, Iran. [email protected]
Correspondence: [*] Address for correspondence: Department of Mathematics, Fasa University, Fasa, Iran
Abstract: 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 ‖.‖2 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.
Keywords: Optimization method, Generalized polynomials (GPs), Free coefficients, Fixed coefficients, Control parameters, Fractional differential equations (FDEs)
DOI: 10.3233/FI-2017-1503
Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 443-457, 2017
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